There is definitely the indication here that Jem, being older, is progressing into adulthood. Just before they discover Dill, he and Scout get into a fight. Then, moments later, he does the responsible thing by telling Atticus that Dill has run away. All three children mature throughout the novel, but Scout and Dill still have an innocent and naïve curiosity about the world. “Breaking the code,” in this instance marks a separation. Jem enters the adult world by telling Atticus. Scout and Dill would have preferred to stay in their own world and kept it secret. This separation, Jem/Scout and Dill, marks the moment the break of that remaining code.