Is it permissible for a student to use a classmate's code to download textbooks from the school's website without his knowledge, given the student's inability to pay the required fees for obtaining the books, and knowing that his classmate will not be harmed by this?

Since the school requires payment of fees to obtain books, it is not permissible for you to give your personal code to someone else to acquire books through it, even if your colleague permits you. And your colleague's permission last year does not suffice for seeking his permission this year.