Hello chrissparks,
Serial # 224XXX shiped in March of 1921 and 228XXX shipped in March of 1923. Your gun should be within a year or two of that time frame. Peter is correct, the guns were not shipped in numerical order but generally follow a time line. Occassionally there is a real outlyer number that is way out of sequence but is not the general rule. If you want to know the exact shipping date and who it was shipped to you can send $50 to Roy Jinks the S&W historian and he can give you that information.
Mark