Author here. We know 128MB codecache was not enough and 256MB was sufficient. I think we could have gotten by with less, e.g. 200MB, but we stopped experimenting once we found a value that worked.
We don't have a complete understanding of why this app uses so much more codecache than other apps we've switched to Java 8. Now that we expose the codecache size in Datadog, I may try plotting code size vs codecache size for a variety of our apps.