EDIT

The git repos need an access control and a general management layer.

Gitolite seems to be the best choice: http://gitolite.com/gitolite/

https://git-scm.com/book/de/v1/Git-auf-dem-Server-Gitolite

Gitolite can also be integrated into redmine:

https://www.redmine.org/plugins/redmine_git_hosting
http://redmine-git-hosting.io/get_started/

Maybe it makes sense to install this redmine plugin so that all important functionality is available from within one application.

IMPORTANT: For using redmine-git-hosting it is highly recommended to run redmine with nginx, NOT with apache, see http://redmine-git-hosting.io/how-to/install-redmine/