I'll tell you this straight: if I'm looking for any level of programmer, I am not wasting time reading every single applicant's code samples. That takes a lot of time and, if I do it and like your code but then don't like you then I've wasted that time. It's much quicker to figure out if you're going to fit than to figure out if you're any good, so I will do that first.
However, for a final interview, I want to see your code desperately (or at least for one of the seniors to see it). I've already decided I like you by then. I need to know how good you are before we decide we're going to make you an offer and how much it will be. Then I'll be asking to see it, you don't need to convince me.
So the question is, "how do you make yourself stand out at the CV stage?", how do you get me to interview you in the first place? As a senior, there are a whole bunch of things you can put in your CV to explain your career path, but as a graduate there aren't.
So you should put your qualifications up there at the top, front and centre. If I'm looking for a graduate then this is what I want to know about first (I would say the opposite of a senior, put them at the back, if they're impressive enough to bother). If I'm relatively impressed by that then I'll read the rest of the CV. In there, a summary of personal projects you've worked on is good.
No code, just what and why, most importantly what problem were you trying to solve. A proven ability to translate problem to solution is invaluable. Also a list of your technology stack. If you're using source control, unit tests and maybe a CI server on personal projects then you're going to get my attention.
Edit: Also links. If you have active web sites or applications, link me to them in your CV. I can't resist clicking, though I won't copy/paste a URL. I won't spend long there, but it's possible to get my attention on the first page. Particularly if you have a blog and any of the subject titles touch on issues that I have recently run into then I'll notice that and look a bit deeper, and if you make sense then I'll remember you when I'm looking back at who to interview.