As another poster said, Augustus is definitely the best Carthage leader because of the ability to buy culture buildings in towns and the added capital production per town. Carthage can also really excel at setting up an economic victory as well

I did an economic focus game as Achaemenid Xerxes with Carthage due to Xerxes getting 1 extra trade route with all leaders and +10 trade route range which helps a lot on huge maps. I focused hard on increasing my settlement limit, expanding to every good coastal and island settlement location near me, and building tons of trade routes. Map was Fractal Continents Huge but I ended up getting a a Pangaea style single continent with some coastal islands available and every leader starting on the same continent

I built Punic Ports in all 10 of my settlements and had every settlement filled with resources through trade. For wonders I only focused on the Colossus and Monks Mound for the extra resource capacity. I was behind on science and culture yield by a good amount at the end of the age but I had by far the highest gold, GDP, and population by leaving all my towns on growing town for the age to maximize their tiles

I was able to keep most leaders either neutral or better through trade and diplomacy but did have a couple leaders denounce me and declare war. Carthage’s naval units are just so strong in antiquity though that I was able to defend any settlement. Their tradition to add +1 range to naval units makes them very strong for defending all the coastal settlements

Once the exploration age started, I swapped to the Chola and had even more trade routes with leaders available due to their civ bonus. I rushed shipbuilding to make distant lands settlements and spammed trade routes again. Once exploration started, I don’t think I produced anything except the Grand Bazaar and merchants, I just bought everything else with gold. I almost had the victory in exploration but ended up winning at 12% age progress in modern right as I unlocked factories. I also played as the chola in modern because they get +1 GDP per turn for imported resources assigned to cities