To me it sounds like the simplest way to expose your git repository on the server (which seems to be a Windows machine) would be to share it as a network resource.
Right click the folder "MY_GIT_REPOSITORY" and select "Sharing". This will give you the ability to share your git repository as a network resource on your local network. Make sure you give the correct users the ability to write to that share (will be needed when you and your co-workers push to the repository).
The URL for the remote that you want to configure would probably end up looking something like
file://\\\\189.14.666.666\MY_GIT_REPOSITORY
If you wish to use any other protocol (e.g. HTTP, SSH) you'll have to install additional server software that includes servers for these protocols. In lieu of these the file sharing method is probably the easiest in your case right now.