In the context of a living being, different genes interact with each other as well. For example, you have certain cells that secrete hormones (many genes needed to do that), then you have genes that encode for hormone receptors, and those receptors trigger other actions encoded by other genes. There's probably too much complexity to ask an AI system to synthesize the entire genetic code for a living being. That would be kind of like if I asked you to draw the exact blueprints for a fighter get, and write all the code, and synthesize all the hardware all at once, and you only get one shot. You would likely fail to predict some of the interactions and the resulting system wouldn't work. You could only achieve this through an iterative process that would involve years of extensive testing.

Could you use a deep learning system to synthesize genetic code? Maybe just single genes that do fairly basic things, and you would need a massive dataset. Hard to say what that would look like. Is it really enough to textually describe what a gene does?

With text and images you can leverage “ground truth” data (verified by humans) to train your model.

The DNA sequences I would look for methods that don’t require good ground truth data.