The libre barcode128 font seems to be a open source copy of the ID family of barcode fonts. So the character codes may match.
Optimized 128 codes (which switch between Code128B and 128C to allow for shorter barcodes if consecutive digits are used in the input string) will not be very human readable, so using them with the font that includes human readable characters will not give great results because the Code128C encoding (For numbers) will mangle consecutive numbers.
I found this librebarcode project on github where someone used a big javascript array with the character maps for the font and the weights you should use for the calculation of the checksum.
Together with the example code and the wikipedia page for code 128 you should be able to get something working in Acrobat.
Here is the array:
var data = [
// the unicode chars are from:
// www.idautomation.com/barcode-fonts/code.128/user-manual.html
// http://www.jtbarton.com/Barcodes/Code128.aspx
// checksum value, pattern, canonical id/name (based on Code Set B)
// (name of the glyph in the font?), [unicode chars], textbelow_flag_or_charcodes
[ 0, ' ', ' ', '00', 'Â']
, [ 1, '!', '!', '01', '!']
, [ 2, '"', '"', '02', '"']
, [ 3, '#', '#', '03', '#']
, [ 4, '$', '$', '04', '$']
, [ 5, '%', '%', '05', '%']
, [ 6, '&', '&', '06', '&']
, [ 7, "'", "'", "07", "'"]
, [ 8, '(', '(', '08', '(']
, [ 9, ')', ')', '09', ')']
, [ 10, '*', '*', '10', '*']
, [ 11, '+', '+', '11', '+']
, [ 12, ',', ',', '12', ',']
, [ 13, '-', '-', '13', '-']
, [ 14, '.', '.', '14', '.']
, [ 15, '/', '/', '15', '/']
, [ 16, '0', '0', '16', '0']
, [ 17, '1', '1', '17', '1']
, [ 18, '2', '2', '18', '2']
, [ 19, '3', '3', '19', '3']
, [ 20, '4', '4', '20', '4']
, [ 21, '5', '5', '21', '5']
, [ 22, '6', '6', '22', '6']
, [ 23, '7', '7', '23', '7']
, [ 24, '8', '8', '24', '8']
, [ 25, '9', '9', '25', '9']
, [ 26, ':', ':', '26', ':']
, [ 27, ';', ';', '27', ';']
, [ 28, '<', '<', '28', '<']
, [ 29, '=', '=', '29', '=']
, [ 30, '>', '>', '30', '>']
, [ 31, '?', '?', '31', '?']
, [ 32, '@', '@', '32', '@']
, [ 33, 'A', 'A', '33', 'A']
, [ 34, 'B', 'B', '34', 'B']
, [ 35, 'C', 'C', '35', 'C']
, [ 36, 'D', 'D', '36', 'D']
, [ 37, 'E', 'E', '37', 'E']
, [ 38, 'F', 'F', '38', 'F']
, [ 39, 'G', 'G', '39', 'G']
, [ 40, 'H', 'H', '40', 'H']
, [ 41, 'I', 'I', '41', 'I']
, [ 42, 'J', 'J', '42', 'J']
, [ 43, 'K', 'K', '43', 'K']
, [ 44, 'L', 'L', '44', 'L']
, [ 45, 'M', 'M', '45', 'M']
, [ 46, 'N', 'N', '46', 'N']
, [ 47, 'O', 'O', '47', 'O']
, [ 48, 'P', 'P', '48', 'P']
, [ 49, 'Q', 'Q', '49', 'Q']
, [ 50, 'R', 'R', '50', 'R']
, [ 51, 'S', 'S', '51', 'S']
, [ 52, 'T', 'T', '52', 'T']
, [ 53, 'U', 'U', '53', 'U']
, [ 54, 'V', 'V', '54', 'V']
, [ 55, 'W', 'W', '55', 'W']
, [ 56, 'X', 'X', '56', 'X']
, [ 57, 'Y', 'Y', '57', 'Y']
, [ 58, 'Z', 'Z', '58', 'Z']
, [ 59, '[', '[', '59', '[']
, [ 60, '\\', '\\', '60', '\\']
, [ 61, ']', ']', '61', ']']
, [ 62, '^', '^', '62', '^']
, [ 63, '_', '_', '63', '_']
, [ 64, 'NUL', '`', '64', '`']
, [ 65, 'SOH', 'a', '65', 'a']
, [ 66, 'STX', 'b', '66', 'b']
, [ 67, 'ETX', 'c', '67', 'c']
, [ 68, 'EOT', 'd', '68', 'd']
, [ 69, 'ENQ', 'e', '69', 'e']
, [ 70, 'ACK', 'f', '70', 'f']
, [ 71, 'BEL', 'g', '71', 'g']
, [ 72, 'BS', 'h', '72', 'h']
, [ 73, 'HT', 'i', '73', 'i']
, [ 74, 'LF', 'j', '74', 'j']
, [ 75, 'VT', 'k', '75', 'k']
, [ 76, 'FF', 'l', '76', 'l']
, [ 77, 'CR', 'm', '77', 'm']
, [ 78, 'SO', 'n', '78', 'n']
, [ 79, 'SI', 'o', '79', 'o']
, [ 80, 'DLE', 'p', '80', 'p']
, [ 81, 'DC1', 'q', '81', 'q']
, [ 82, 'DC2', 'r', '82', 'r']
, [ 83, 'DC3', 's', '83', 's']
, [ 84, 'DC4', 't', '84', 't']
, [ 85, 'NAK', 'u', '85', 'u']
, [ 86, 'SYN', 'v', '86', 'v']
, [ 87, 'ETB', 'w', '87', 'w']
, [ 88, 'CAN', 'x', '88', 'x']
, [ 89, 'EM', 'y', '89', 'y']
, [ 90, 'SUB', 'z', '90', 'z']
, [ 91, 'ESC', '{', '91', '{']
, [ 92, 'FS', '|', '92', '|']
, [ 93, 'GS', '}', '93', '}']
, [ 94, 'RS', '~', '94', '~']
, [ 95, 'US', 'DEL', '95 ', 'Ã']
, [ 96, 'FNC 3', 'FNC 3', '96', 'Ä']
, [ 97, 'FNC 2', 'FNC 2', '97', 'Å']
, [ 98, 'Shift B', 'Shift A', '98', 'Æ']
, [ 99, 'Code C', 'Code C', '99', 'Ç']
, [ 100, 'Code B', 'FNC 4', 'Code B', 'È']
, [ 101, 'FNC 4', 'Code A', 'Code A', 'É']
, [ 102, 'FNC 1', 'FNC 1', 'FNC 1', 'Ê']
, [ 103, 'Start Code A', 'Start Code A', 'Start Code A', 'Ë']
, [ 104, 'Start Code B', 'Start Code B', 'Start Code B', 'Ì']
, [ 105, 'Start Code C', 'Start Code C', 'Start Code C', 'Í']
, [ 206, 'Stop', 'Stop', 'Stop', 'Î']
]
;
My own semi-working experiment is up on GitHub if you want to try.
