I have what might be considered an asset pack or (multiple asset packs), that comprise of generic code I wrote for save systems, events, inventory, sounds etc. They're not a paid asset because its not for sale anywhere but I wonder if its allowed?

2 things would make it clear if it's allowed or not:

1) Did you write those codes?

A better question would actually be "Do you understand everything about those codes?" If you can answer "yes", then using existing codes is allowed as long as you properly implement them in your project. (Or at least, it's what was explained around.) Ideally, you should avoid just using full bundle of existing codes and only use the lines you actually need. For example, there might be questions if the codes includes notes about features that are totally not in the game or store data that is unused and irrelevant to the game itself just because they were in your base code at the beginning. You should take the time to clean up the codes before submitting your project at the end.

Do you really think that you got time to make a bunch of events and an inventory system (meaning a whole database of items) for your project in only 10 days?

2) Does those packs includes full systems with assets or are they just codes to build new ones?

Using existing lines of codes is allowed, but using full-made systems is not. For example, you could use a radar system, but then you will have to do all the visual image during the 10 days. All the UI, images/textures, mesh, animations, etc. has to be either made during the 10 days or be available on the public domain for everyone. You should also watch out with those sounds unless you made them yourself or you know they already came from a public domain listed source of assets.

This returns to the 1) above with an inventory system. In 10 days, I doubt you'll have time to make loads of icons (and, if applicable, meshes) for items on top of implementing an actual usage of items.

Using existing codes is allowed, but using existing models, textures, sounds, musics, etc. that are not on the public domain is not. (Or at least, it's what been told around.) You can't just modify existing stuff you found online either. Ultimately, all the asset have to be made during those 10 days or be on the public domain.

I'm not part of the judges, but I read around and those are the general points about the question. If I'm wrong, I would invite any actual judge at specifying whatever rule about this.