Codacy supports badges you can integrate into your projects to show your project code quality level.
You can add a badge directly to your repo by clicking the option "Share" directly in your project dashboard.
If you go to your project 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".