[POPE] DAMASUS, 366-384.
6. In his episcopate, Valentinian I enacted a law making the bishop of Rome the judge of other bishops. A council in Rome, A. D. 378, enlarged his powers of judging, and petitioned the emperor Gratian to exempt the bishop of Rome from all civil jurisdiction except that of the emperor alone; to order that he be judged by none except a council, or the emperor direct; and that the imperial power should be exerted to compel obedience to the judgment of the bishop of Rome concerning other bishops. Gratian granted part of their request and it was made to count for all.
Source: Ecclesiastical Empire, by A. T. Jones, Review and Herald Publishing Co., Battle Creek, Michigan, 1901, pg. 157.
The development of the papal power can only be briefly summarized here. The first great step took place under [Pope] Damasus (366-384) who obtained from the Emperor Valentinian I the right of all bishops in the western part of the empire who were condemned by their provincial synod to appeal to the Bishop of Rome.
Source: THE CHRISTIAN FAITH: AN INTRODUCTION TO DOGMATIC THEOLOGY, by Claude Beaufort Moss, D.D., London S.P.C.K, 1965, Holy Trinity Church, Marylbone Road London, NW 1, Printed in Great Britain by Richard Clay (The Chaucer Press) Ltd Bungay Suffolk, first printing 1943, Part II, Chapter 49, III. The Papacy a Development from the Order of Bishops, 1. Origin and Development of the Papacy. aloha.net