Your github repository is the only evidence that's available to them that you can write or design anything. Yes, your github contents could use improvement. I put mine up as a motivator to me to improve on my software engineering capabilities. My github is woefully out of date but I get a kick out of seeing where I am compared to where I was. Showing something is better than showing nothing, as long that the something that you show is a positive, like your competence :)
Plus, your github link is your way of saying that you know how to use github. Actually, I had to learn the github internals to do that but that'sanother story for another day. At the very least,publishing your github account should motivate you to learn as much as you can about github. There is no uch thing as being too good at github :)
Being a good software engineer is a process not a termination point to a process. As you improve and get to be wylier as a problem solver, your github contents become more sophisticated. And no, the process doesn't have an end point :)
In terms of what to publish, code that highlights your grip on the fundamentals is fine. Junk is not. The line between good stuff and junk can be blurry. My standard is that I don't publish anything that I cannot justify as publishable.