I fear that I neglected that for too long. I don't know what is complex enough to impress anyone, but I doubt I can hack something together in under a month that will reach that level.
The point of this is to market yourself as an Actual Programmer, and it doesn't take much time or effort to reach that point. (Although, in my case, I was distinguishing myself from the plethora of generic comp sci students, and you might have a higher barrier.) After all, whoever hires you will _really_ judge based on how well you interview, which is just a few hours of your life.