Hi Tom,
a 16 characters x 4 lines display, believe it or not, has to be initialised as a TWO lines display. This has to do with how the 44780 is designed internally.

The first line starts at $00h,the second line starts at $40h.
In fact, the third line is continuous to the first line, and the fourth line is continuous two the second line (from addressing point of view).
So line 3 starts at $10h, and line 4 starts at $50h.

Code to drive the module in 8bit modus has to be find easily on the internet.

Henk