Improve Docker layer caching for Go dependencies (#560)

Running `go mod download` before copying the entire project to the
Docker image avoids dependencies from being re-downloaded every time any
file is modified, and `docker build` runs again.

This follows the steps detailed in the official Docker guide for Go
images:
https://docs.docker.com/language/golang/build-images/#create-a-dockerfile-for-the-application

Also, `GO111MODULE` doesn't make any difference for the supported
Go versions, so it can be removed from the Dockerfile.