Given the effort required by Jor-El to acquire, transfer and protect the genetic information of the Codex, as well as transferring some aspects of his scientific ability to a data-key, it should be assumed he had some plan for the information of the Codex, even if he never mentioned it during the movie.
Jor-El is a thoughtful individual and his world's premiere scientific mind. He understood both the perils Krypton faced and the ultimate fate of his people, for they were both hidebound and stubbornly traditional.
They were so bound by tradition, they abandoned their space colonies centuries ago and retreated to their world. They refused to leave that world even when it was at least a theory that Krypton might be unstable and potentially destroy them all.
With this as the premise, Jor-El steals the Codex, the DNA matrix of every Kryptonian trait and potential seed to repopulate the species if a birthing matrix can be found. He encodes this information within his son's DNA.
Given the existence of former Kryptonian outposts and gene-ships like the one found under the Arctic ice on Earth, it would be safe to assume Jor-El did indeed plan for Kal-El, once he reached adulthood and had the intellectual capacity to do so, take the Codex information and seek out a gene-matrix ship and recreate the Kryptonian species.
I base this supposition on the fact there was no other reason for Jor-El to take the time to gather the Codex in the first place. Despite his dislike of the genetic technology used by the Kryptonians, even he could see in this instance, it could have a place in saving their species, giving the Kryptonians a second chance.
Since there would be plenty of technology out there, all it would take was a data key like the one used to guide Kal-el's ship and store Jor-El's consciousness. The Phantom Zone criminals found such technology and even took some with them to Earth. The Krypto-forming World Engine was one such piece of technology. There appeared to be plenty of such technology available on the site the Zod raided.
With the loss of the key and Jor-El's consciousness, it is unlikely, that Kal-El will be able to command or control a gene-ship (assuming he could find one) in order to release the genetic information for a new generation of Kryptonians.
