The N and the broken I are apparently some Remington inspector's marks. I can barely see one letter of the date code. Yellow arrow --
16-gauge Skeet Gun.jpg
Here is an example of a barrel flat with the N and broken I but a clear view of the date code.
238463 01 VH 20-gauge, 26-inch, AE A = March E = 1936.jpg
AE A = March E = 1936.
From my observations, while still in Meriden they put the date code for the barrels near the rear as above. After the move to Ilion they started putting the date code farther forward abreast the cocking hook.
241968 01a 26-inch, 16-gauge, XJ X = December, J = 1940.jpg