Jor-El had discovered that the planet faced imminent destruction. The council however refuted or refused his claims. Zod takes note of how the Council has dismissed the claims and decides to overthrow the council as he feels that they are not governing properly. He felt that the council members are involved in petty politics, daily affairs and their own well being. When they should be more concerned about the planet and should at least have paid attention of Jor-El's claims. Also, none including Jor-El could have known that they planet would die so early. They only knew that it would happen soon. Jor-El always planned for his son to escape to Earth to be saved from the planet's destruction.
Zod however, planned to overthrow the Council and take control of the Codex to save the planet's race. There was no such plan. The planet was destroyed soon after he started the coup. He initially planned to take help of Jor-El to prepare a plan for survival. However, this required that the council be overthrown first. Zod would then take control of the Codex, and ensure that only proper bloodlines were produced.
His initial plan was to take control of the Codex, and to choose proper bloodlines for further propogation. He also tried to enlist Jor-El as he had significant knowledge and means to ensure the survival of the kryptonian race
In a doomed planet, it is not possible to save all the population. However, with the Codex and the technology at hand (genesis chamber), Zod could save the Kryptonian race. That was his only plan at the moment.
Jor-El travels to Kandor on his pet H'Raka where he stands in front of the Kryptonian Law Council telling them the planet is to explode because of the council's decision to harvest the planet's core to serve the depleted energy reserves of the planet. They dismiss his claims but General Zod takes note informs Jor-El he is going to overthrow the council. from Man of Steel - Superman wikia