Carthage is a nation that controls most of Africa. Auedi pays tribute to it and its only real enemy is Rome.
The main idea of Carthage is to colonise Iberia, and you should get that as your first mission. At the start Rome is much more powerful than you, so you will need to grow and make friends with another large power - Egypt should do nicely.
You are separated from the Romans by the sea. As long as you have naval supremacy, they won't be able to land their troops on your shores. Colonise Iberia and proceed from there, Rome shouldn't be a serious threat unless your navy dies. The real threat to you is the Seleucid Empire. If they manage to defeat the Egyptians, they will share a land border with you and with their massive manpower they will walk all over you. Maintaining naval supremacy should be your number 1 priority.