I couldn't run the Docker image, it seems that the Java process running in docker image doesn't bind the port 3000. Also tried to deploy to Heroku but when I try to access the application via url, Heroku throws 503 error.
You can double check that we are exposing port 3000 from the container which is where the app is designed to run by default. The Dockerfile used to build the image is in our repo here: https://github.com/metabase/metabase/blob/master/bin/release...
Heroku sometimes times out if the application takes too long to start. Could you try again and see if it works? We're working on making Heroku deploys more robust.