Test build with Docker automatically

From time to time, we have problems with our Docker build (docker/build.sh). Unfortunately, these problems aren't always reproducible for different contributors which means that they aren't noticed when a PR gets tested manually, but only later after a contribution was already merged to a release branch.

Here is a recent example.

We should use Travis to also execute the Docker build automatically. That will hopefully at least find some problems like this before it gets merged.