Jor'El was one of their leading scientists. I would presume that he had access to it to begin with?
If Jor-El had access to the Codex, why was he challenged by a robot threatening him with a class B offense for taking it?
If he didn't have access to it, why was the greatest trouble he had to go through to get his hands on it apparently only swimming underwater?
I think there is a difference between being allowed access to something and being allowed to take it.
If Jor-El was allowed to access the Codex at all, then why did he have to swim underwater to get to it? (ETA: My point is that the chamber didn't seem intended for anyone to access it at all. Was there no way to get to it without going underwater?)
It seems the intent was that he was not allowed to either access or take it, at least at that time. However, the safeguards to prevent Jor-El from acting in unauthorized ways around the Codex were minimal to non-existent.
Now, I suppose there could have been only minimal safeguards, because Kryptonians just weren't expected to act outside the purviews of their castes. On the other hand, they did have the Phantom Zone, so crime was not a foreign concept to them. The Codex had to be among the most critical artifacts of their entire culture, so it's hard for me to assume that it wouldn't occur to them to protect the Codex.
Perhaps Jor-El nullified some of the security, but I just don't recall anything like that happening. I'll keep my eyes open on next viewing.