Do you think you could get it to prefer the left-down-up strategy as described elsewhere in this thread? (Personally, I used left-down-right, but it's all the same). Then it should be possible to increase the chances of reaching 4096. I myself have reached 8192 with that strategy and heard about other people getting to 16384.
One easy way would be to skew the AI evaluation score heavily towards states with lower numbers of tiles. Maybe log(score) - num-tiles?
My main goal was to create a player without embedding any human developed strategy (such as left-down-up). This would obviously be less optimal but more general purpose.
If you are interested in domain specific algorithms, the same StackOverflow question I linked features a solution using a min-max variant using an elaborate hand-crafted scoring function. It's best run scored 794076 points and got the "32768" tile.
One easy way would be to skew the AI evaluation score heavily towards states with lower numbers of tiles. Maybe log(score) - num-tiles?