MantisBT is free software. We encourage you to dive into the source and help on new features and bugfixes. That is the way free software works.
Here are some important pointers for MantisBT-Development:
MantisBT source code is hosted on GitHub. Detailed information on how to use git with MantisBT can be found in the Mantis Bug Tracker Developers Guide. Help with setting up Git and learning basic usage can be found in GitHub's Help pages.