With overwhelming power on their side, the Kryptonians did not care in the least about humanity's opinions. General Zod broadcast his message to the entire world. He was searching for Kal-El—Superman Clark—because Superman's father, Jor-El, had stolen Krypton's greatest treasure, the Life Codex, before Krypton's destruction and sent it away with Kal-El.
General Zod had been born for one purpose alone: to protect Krypton and its people. For that, he had even been willing to launch a coup in an attempt to save the Kryptonians.
But after General Zod's coup failed, he and his followers had been imprisoned in the lightless Phantom Zone. Only when Krypton was destroyed had they managed to escape.
By then, Krypton had already been destroyed, and every Kryptonian on the planet had perished.
The blow this dealt General Zod was unimaginable.
With his remaining subordinates, he set out on the long road to rebuilding Krypton.
They knew there was still hope. The Life Codex was still with Kal-El—Superman. As long as they recovered it, they could rebuild the great Kryptonian civilization on any planet.
That became the faith sustaining the dozen or so surviving Kryptonians.
General Zod and his group of more than ten people had continuously searched abandoned outposts for anything they could use. Fortunately, they found the World Engine, a machine Kryptonians used to transform planetary environments and alter a planet's atmosphere to make it more suitable for Kryptonian survival.
At the same time, the World Engine could perform spatial transportation, allowing them to travel rapidly through the universe.
Searching abandoned outposts for usable supplies had been tedious and dull work, but it was something General Zod and the others had no choice but to do. Countless ruined outposts served as constant warnings, leaving them forever tormented by the loss of their homeland.