You can start a container with your Docker executable and socket as volumes like so:
docker run -v /usr/bin/docker:/usr/bin/docker -v /run/docker.sock:/run/docker.sock -i -t ubuntu /bin/bash
In that container, you can run docker images
as test to see you can do any Docker command you deem fit, like building and uploading to the registry. I use this myself to run a Jenkins slave with Docker capabilities.