I don't think I've ever seen a coder (as opposed to "UI guy/gal" or graphic designer) come in with a portfolio. Usually it's just a resume that lists out previous projects, which you then get grilled about. So it's not an absolute requirement.
But I also don't think it would hurt to have some project you could point to, even if it's not something incredibly innovative. There are people out there that are smart, but don't actually get anything done. So it's worth proving that you're smart and can get stuff done. It would also give you something to talk about in the interview that you know inside and out, which is usually a lot easier than discussing contrived examples or academic problems. Even if you go code something fairly trivial (eg,
IsThereAFuckingRockiesGame), it's a starting point. You can then talk about challenges in building it, what you liked/didn't like about technologies you used, etc. If you do choose to do a sample project, post the code on Github. If nothing else that demonstrates familiarity with source control, which is important and sometimes overlooked in academia.
Other common recommendations are contributing to an open source project, or doing coding contests like TopCoder. Those might be good options, but I haven't tried them and haven't seen anybody put them on a resume that I've seen.
But no matter what, SeattleCyclone is right that you'll have to code on a whiteboard. I have seen guys with literally decades of experience and their names on products with 100k's of paid users subjected to "write mergesort on a whiteboard" style interviews. So it's worth learning how to do that.
You might also consider looking into remote/work-from-home positions. They are generally scarcer than show-up-at-the-office jobs, and might be difficult to find as entry level positions. But it sounds like you can afford to spend a little time looking into it and see if anything comes up. There are a few websites out there that specialize in remote work job listings. Also I believe StackOverflow Careers has a search filter for that. Don't be shy about looking at internships as well - many software internships are of the paid variety, and sometimes the well-paid variety.
As a person working in the industry, how should I leverage my current job as far as experience?
Try to talk about what you learned that might transfer. That can definitely include soft skills like dealing with angry people or written communication. Those skills can be quite valuable but are frequently overlooked in preference to checking boxes for programming language. Actually, what does "IT Security operational work" involve?
Also, if you have the choice, it's generally better to work at a software company rather than in IT for a company that does something else. In software companies you're creating revenue, in other companies you just an expense (read: necessary evil). So you'll usually get better pay, better perks, and more security at software companies. There's nothing at all wrong with IT work, I did that for years myself, it's just that non-IT work is usually better if you can get it.