Learn Finnish: Te opiskelitte koodia muistaaksenne sen huomenna. - You studied the code to remember it tomorrow.

It means "in order for you to remember". It is built from the basic dictionary form of the verb muistaa (to remember), plus the marker -kse- which adds the meaning "in order to", and finally the possessive suffix -nne which matches the subject Te (you plural).

Could I just use the word jotta (so that) instead of muistaaksenne?

Yes! This grammar structure is just a shorter way to express purpose. Saying jotta te muistaisitte sen (so that you would remember it) means exactly the same thing, though the -kseen structure is very common and sounds a bit more fluent.

Why is the code in the partitive case (koodia) in the first half of the sentence?

The verb opiskella (to study) expresses an ongoing, continuous process. In Finnish, verbs that describe an incomplete or continuous action require their object to be in the partitive case.

Why does the pronoun for "it" take the genitive form sen in the second half of the sentence?

Unlike studying, the verb muistaa (to remember) is treated as a completed result. Because of this, its object takes the total object case, which looks like the genitive (sen) here. It shows that the goal is to remember the code completely.