The top barrel rib on a model 14/K-38 Masterpiece is wide, but the one on a model 15/.38 Combat Masterpiece is narrower.
S & W made intermittent runs of 4" K-38s and yours may be one, or it may have had the shorter barrel installed. It was probably made in 1958 but its official birthdate (and whether it is original) would take a letter of authenticity to confirm.
http://www.swhistoricalfoundation.com/swhf_letter.pdf