I disagree. A neural network is not learning it's source code. The source code specifies the model structure and hyperparameters. Then it compiled and instantiated into some physical medium, usually a bunch of GPUs, and weights are learned.

Our DNA specifies the model structure and hyperparameters for our brains. Then it is compiled and instantiated into a physical medium, our bodies, and our connectome is trained.

If you want to make a comparison about the quantity of information contained in different components of an artificial and a biological system, then it only makes sense if you compare apples to apples. DNA:Code :: Connectome:Weights