From Hodgdon website for 223 with 77gr bullet:

IMR IMR 8208 XBR .224" 2.260" 20.5 2,535 41,800 PSI 23.2 2,792 55,000 PSI

I would start at 22gr and go up in 0.3gr increment: 22.0, 22.3, 22.6, 22.9, 23.2. Five rd groups for each.