The one Eileen and I have been using in the .22-250 for a few years now is the 70-grain Hornady GMX, which has worked great out to 350 yards.
Of course, Hornady just discontinued the GMX bullets--and replaced the line with their new CX bullet, which is all-copper and features their heat-resistant plastic tips. But so far they're not listing any .224 CXs. Luckily, I have a good stash of 70 GMXs!
