He might have been the "generous Anicius" who was the first Senator of high rank to become a Christian.

Sextus Anicius Faustus Paulinus

Sextus Anicius Faustus Paulinus (fl. 325–333) was an aristocrat of the Roman Empire. The offices he is known to have held were: Proconsul of Africa Province; consul with Julius Julianus as his colleague in 325; and between 331 and 333 praefectus urbi.

A member of the gens Anicia, his father was probably Anicius Faustus Paulinus and his brother was Amnius Anicius Julianus (consul of 322); Amnius Anicius Paulinus was probably his son or his grandson, or the son of his brother. Perhaps he is to be identified with that Anicius who was the first senator of that lineage to publicly convert to Christianity.

Source :

https://en.wikipedia.org/wiki/Sextus_Anicius_Faustus_Paulinus_(consul_325)