I told my boss I had an idea for a program that could improve efficiency across much of the business, and he let me build it on company time. In the long term, he wanted to be able to sell it to other companies. However, the program never got implemented due to personnel mismanagement, and I'd rather be able to post it on my github under a free licence so I can use it as a resume item, and at least someone would have the chance to actually use it. It's all still in my head, and I could write it again if I wanted. If I do, is it illegal to publish it? What if I write it in a different language? Do I need to change the variable names? I did plenty of research and planning on company time to build it, and it's not like I can research it again, it's all still in my head.
It depends in the country you are.
If you want to show of your skills, why not write an article about it. This way you don't publish company property (maybe only snippets of code) and the viewer can read your reasons on why you made certain decisions.
But do not do this without consent of the company. If the company likes it, you could even start your article something along the lines of "here at %company% we like to write good code…". Than it is a win-win. I see this a lot on sites like medium.com