Programming touches both comprehension of the code and the world it interacts with. Any program which can write programs based on comprehending natural language ought to be able to rewrite itself. Can you please explain how what you are describing is distinct from AGI?
I view current deep learning as a cumbersome counterpart to retina-level cells (well, from 30,000ft). Anyway, DL can roughly do what a few specialized biological neurons can do, like in the case of retina identifying direction, speed etc. It's far far away even from a whole brain of an insect, but it can do some amazing things already. Here what you can do is to utilize those things it can do (and they will be getting better), and add some human-made inference/anotation/ontology/optimization system on top of these partial components. The human-made system can be chipped away slowly as we figure out how to automate more and more of its functionality.
So for example, for simple programs you don't need to understand what individual code blocks are doing. All you roughly need are some well-defined procedures/visual components (able to ignore unsupported operations) that can be composed LEGO-style. Here AI can learn to associate certain compositions of code blocks with your sentences, e.g. you can teach it with touch what does it mean to resize, move to left, change color etc., and even provide those code blocks. To help it, you have to annotate those code blocks so that you maximize chance of valid outcomes. ML by itself is not capable of inference, so inference must be done differently. Yet what your AI learns with associating certain sentences with outcome in your code blocks will persist. And for making associations you can unleash millions of developers that might be working on your goal unknowingly, e.g. by creating a safe language like Go for which you have derived nice rules that you can plug into your system. Initially you could only to pretty silly things, but the level of its capabilities will be rising all the time and there is a way forward in front of you, even if a bit dimmed.