Hi MAS3, and thanks for you answer !
You are right about the exact name, changed it...
First of all I tried the LiquidCrystal library with this settings - lcd.begin(24, 2), using 4-bit and 8-bit wiring, but there was nothing in the display (only upper line of rectangles).
It seems some problem with LCD pin out (maybe some difference with the data sheet), or LCD just is not HD44780 compatible and demands another initialization/commands.
BTW, the code I attached above works perfect with standard W1602 connected to the same UNO board.