Not sure if you worked out an answer to this, but there's no magic button that will solve your problem.
However, InDesign does have a facility in each Paragraph style called GREP that can do what you're looking for.

This lets you write 'regex' or 'regular expressions' that are just rules for what to apply a given character style to. Yes, they look about as meaningful as Harry Potter incantations at first glance, but 2 or 3 simple regexes will get you a long way.
For instance:
(\<|<)!--\s*.*?\s*--(\>|>)
Will target HTML comments only.
(?<=").*?(?=")
This will target anything wrapped in straight double quotes.
(?<=\().*?(?=\))
This will target any text inside parentheses ().
There's an '@' symbol button in that GREP style next to where you type the regex - that gives you a drop-down menu that is almost like a 'Regex Wizard'. Try that too.
When you've got a regex that works, create a new character style for the text color and select it in the 'Apply Style' input.
Regexr.com has a tool that is good for testing this stuff. Paste your code sample in the bottom panel and your line of regex in the top. The bits that it targets will turn blue.
There is a searchable community panel on the left where people have probably already written expressions like the one you need.
I'm working out a JavaScript highlighter at the moment. It's a shame there's no communal 'Indesign style sharing library'.
Best of luck.