Not a lawyer, but worked closely with them in the past. It REALLY depends on your employment contract. Changing variable names and language still makes it a derivative work, so it would depend on the original license. I'm assuming it doesn't have a license which would mean either you or the company owns the copyright: depends on your employment contract. Whether you're a contractor or full time also affects ownership.
Without ownership or a license, you do not have the legal right to copy the work or make a derivative of it.
I'm not clear on whether you actually wrote any code though. If that's the case (that no code was written) then I'm not really sure how that works out. If you do post it and they find out, AND they're mad about it, you could definitely get fired. I'm not sure if there could also be legal trouble or not.
If you need it for a resume item, you can just list it on your resume and talk about it. You could also implement it on your own time (but not share it until you're sure you're safe from legal action), that way you could talk about tradeoffs you've made, etc. in the real implementation.
In general, if you're not sure and you're worried about getting sued, you should ask a lawyer.
Yes, though this is true of a lot of the easier distros.