Embedding git commit into the resulting data

Our pipeline works something like that:

1. Collect bunch of raw data (10-100 GB) from microscope
2. Process data using MATLAB scripts
3. Change few parameters based on raw data, as well as add new features to the scripts
4. Commit the scripts with new features to git repo
5. Re-run processing, save results as figures and CSV data (1-10 MBs)

Are there tools available for seamlessly linking MATLAB figures or tabulated data with the code version (git commit hash) that was used to produce it?

I know that MATLAB is aware of git, as well as we can call system commands