This can be stated in active form. Alternate translation: "According to the task that God freely gave me to do" (See: [[rc://en/ta/man/jit/figs-activepassive]])
Paul is referring to the person or people who are teaching the Corinthians at that time as if they are carpenters who are constructing the building above the foundation. (See: [[rc://en/ta/man/jit/figs-metaphor]])