I am working on an Open Source project and I have a git repo on my machine with all the code. The repo is kind of big, and I would like to keep working on it while I do not have
I kinda don't like the idea of copying git repositories from one place to another. Instead, I absolutely would recommend using a remote server for your code.
There's at least 2 excellent git as service around: the most famous is GitHub, which will freely host your code if you don't mind sharing it in a public repository. If you want to keep it private and don't want to pay for it, go for BitBucket.