Automated test of the docker build

@chris48s wrote at https://github.com/badges/shields/issues/2814#issuecomment-455898956:

> I think we should be able to just call `docker run` inside Circle CI. That would at least give a us a smoke test that it doesn't throw an error.

A couple references:

- https://circleci.com/docs/2.0/building-docker-images/
- https://circleci.com/blog/how-to-build-a-docker-image-on-circleci-2-0/

I think ideally what we want is three things:

1. Check that container builds
2. Check that container runs
3. Fetch a badge from the server and ensure it works

We also need a way to shut down the container after 2 or 3 is finished.

Start by locating the repository's CircleCI configuration and the Docker build, run, and server entry points; no specific files or tests are named in the issue. Add checks for a successful build, a running container, and a working badge request, then confirm the container is shut down afterward.

Written by the indexing model from the issue text.