New channel balances

Thanks for posting. The only particularly relevant part of the stamp code is actually the 20-5 part, which tells us your balance's calibration. If both balances in the window have the same nylon fittings, then you need either an S351-21 or S390-21. The only difference between these two balances is the bottom nylon shoe depth, so compare both with your old hardware to see what matches best. The picture below shows more detail. You will need a stamp option of 2050. 

Comparison of the S351 and S390 balance shoes.

Sorry for not noting the sash weight you provided earlier! To be honest, that is definitely weird. Before the balances broke, did you ever have trouble keeping the window closed? Did it drift upwards when unlocked? This is indicative of balances too strong a calibration for your sash's weight. If you are indeed certain the sash weighs exactly 13.7 pounds, go with a stamp option of 2030 (12 through 15 pounds). Apologies for any confusion.