How do I deploy this web app (Sentry) to Amazon Elastic Beanstalk using Docker?

Question

I am trying to deploy a popular web app (Sentry) to Amazon Elastic Beanstalk.

Beanstalk has support for Docker containers and the Docker Hub already has a configuration for Sentry here.

I have tried the following Dockerrun.aws.json:

{
  "AWSEBDockerrunVersion": "1",
  "Image": {
    "Name": "sentry"
  },
  "Ports": [
    {
      "ContainerPort": "8080"
    }
  ],
  "Volumes": [
    {
      "HostDirectory": "/var/app/sentry",
      "ContainerDirectory": "/etc/sentry"
    }
  ],
  "Logging": "/var/log/sentry"
}

However when I upload it to Beanstalk, it fails to deploy it stating "no initialization file found".

I have all the environment variables (SENTRY_SECRET_KEY, SENTRY_DB_NAME, etc) configured in the Beanstalk environment variables as well.

Am I missing something? Do I need to write a Dockerfile instead of a Dockerrun.aws.json?