There were two different serial number ranges for this model. The early 44 Russian NM3 had 11 7/16" cylinder lengths, while the 44 Winchester Frontier Model was 1 9/16" cylinder.
If it has a short cylinder, the gun would have been manufactured the first year of production in 1878. If long cylinder, the first year production was 1885. The picture you posted looks like the short cylinder, but take the measurement and that will help.
Now, let's discuss the target options for this model. Some early serial numbered target NM3s shipped very late, into the 1900s, so there is no way to tell when the official ship date was without a historical letter. S&W and the BATF define antique classification based on when the frames were made, so all NM3s are considered antiques, made pre-1899.