sounds very much like a 9,3x57R 360

brass can be made from 9,3x72R S&B or RWS, original 360 2 1/4" brass is made from Betram and Horneber iirc. be shure about the chamber dimensions when order a die set. it can be that a case sized with a 360 BPE or NE die set will not fit the chamber.

the common .364 bullet for the 9,3x72R may work when the barrel is 363. for plinking you can use 9mm Makarov bullet.