Problem 2266. 2048 tile game

The popular 2048 game has been implemented here:

http://gabrielecirulli.github.io/2048/

Given the board like this:

[2 4 8 0
 4 0 0 0
 2 0 0 0
 2 0 4 0]

You give the direction

1 (left) 2 (up) 3 (right) 4 (down)

The system here will keep calling your solver. Score for each board is the biggest tile achieved. The Cody score is the maximum board score plus the average score across all 200 boards.