Codacy supports badges you can integrate into your repositories to show your repository code quality level.
You can add a badge directly to your repo by clicking the option "Badge" directly in your repository dashboard.
If you go to your Repository Settings -> General tab you have the option to add the badge with your Codacy grade (same as above) and, if you set up Code Coverage, a badge for your coverage.
Creating badges for different branches?
You can do that if in the end of the badge URL, you add the query parameter "branch=BRANCH_NAME".