Using a trajectory calculator, if we neglect air resistance (which, I know, we can't, and it WILL be a big factor, but bear with me) a shell fired at a 45 degree angle at 7920 f/s (= 2414 m/s) would go 594 km, reaching a peak height of 148 km, which is above most of the atmosphere.
And 594 Km = 368 miles. Throw in about 15 miles of air resistance at the start and 15 miles at the end and you get about 200-300 miles range or so.