It's intentionally ambiguous because Jor-El didn't want Kal-El to repeat Krypton's mistakes.
If it were purely up to Jor-El, most likely he'd co-habitate with humanity where the Kryptonians ruled as benevolent gods. The hints we have to that effect:
- Saying Kal will be like a god;
- His speeches to Kal about guiding humanity and saving them all;
- His argument with Zod about co-existing with humanity.
However... despite his
own inclinations, Jor-El knows that he's the product of a fallen culture and likely to pass on those mistakes to Kal-El. Jor-El believes this so strongly he does several significant things:
- He never plans to go to Earth with Kal - for fear of raising Kal with Kryptonian values / issues
- He makes it impossible for Kal to hear from him until he's been raised as an adult - He doesn't leave a message that Kal can access as a child
- He explicitly SAYS both of the above - Can't get clearer that that! He says why he didn't go with Kal and he says why he wanted Kal raised human
- He never tells Kal to use the Genesis Chamber - Instead he explains it as being the downfall of Krypton, it's a warning or a cautionary tale, not an encouragement to use it
- He never tells Kal about the Codex! - This is critical! Even after Zod questions Kal, Clark goes home to Martha and says, "Mom, Zod said this Codex he's looking for can actually bring my people back." Zod never tells him he's the Codex either, so Kal doesn't know he's the Codex!
My interpretation is that Jor-El was worried if he told Kal what it was, that would be paramount to a command or imperative to use it. Instead, Jor-El wanted Kal- raised human and with the interests of both people in mind- to eventually learn about and decide what to do with the Codex.
We can already see from BvS that humanity is deeply interested in Kryptonian biology. It's only a matter of time before Kal discovers the Codex himself
with humanity and
together decide what to do about it.
Outside the film, Russel Crowe gave an interview where he interprets Jor-El as wanting Kal to start a literal Kryptonian-Human hybrid race on Earth as gods, which he- Crowe- calls "a touch of madness." So that suggests how he was playing the character whether or not it comes across. Obviously, Clark wouldn't be on board with that and Jor-El was right not to indoctrinate him into thinking that's the way things should have gone.
