I used to work at GFDL and I know that they provide some code on GitHub, including at least one climate model (MOM6). Also, the Flexible Modeling System (FMS) is core to the work they do, but you'll have to put your Fortran hat on. You might also look at PCMDI's repo. They provide tooling that helps standardize climate data for the international community for use in the assessment reports. For something more on the distribution and analysis side (which may be more accessible and interesting to people who aren’t climate scientists), take a look at the Earth System Grid Federation (ESGF). Hope this helps!
https://giorgiocalderolla.com/wipr.html