Homebuilt engines don't generally make for stunning portfolio pieces. Unless it's enabling you to build something that isn't possible in current off-the-shelf engines, it's probably not a great portfolio project.

Also tends to be the case that having one polished project is worth more than several unfinished ones.

What specific aspect of games programming are you interested in getting into?

While it never hurts to know low-level C++, you're unlikely to get all that much mileage out of it working on enterprise software (most enterprise shops use Java, NodeJS, and so on).

23 minutes ago, Icompose said:

Would it be best to finish my UE4 game at this point?

A programming portfolio needs to have games in it. Finish that one and then make another. If that one is a solo, it would look good to have a collaborative project too.

I wouldn't recommend putting anything in your portfolio that is NOT complete. It must be complete and polished. That'll look good to an employer. Seeing a lot of work is nice, but seeing your determination to complete and fine tune is something that not everyone does. 

Finish your portfolio items!

You may want to check these out for now:

http://www.wartothecore.com/vacancies/vacancy-intern-unity-3d-developer/
http://www.wartothecore.com/vacancies/vacancy-net-developer/

When you apply to full time jobs, make sure you have a good portfolio to show. There are interesting studios in your area, like MS Games studio, Valve, Oculus, 343 industries and others. As always, the portfolio will get you to interviews, from there you need to show your knowledge and problem solving skills.