I wouldn't think you could install the 1614 firmware on a 1604 board (I may be wrong though).
Maybe it has had a newer 1614 motherboard fitted, as I would think the connections would be the same and it should run.
Oh just checked on digiprints site, and the boards are the same!!!!!..
http://www.digiprint-supplies.com/vj-1614-main-board-dg-44332.html
So yes you probably can use the 1614 firmware on this board.
Making your 1604 into a 1614.
I always questioned what made the 1614 supossedly faster than the 1604, and the answer is nothing.
Guess we were lied to all along as the carriage motors are also the same on both machines.
The only difference is you can position the ink carts vertically in the 1614!
SC