BIG UPDATE:

Yeah, I had some problems at the beginning of the jam but I finally did some serious progress:

Now, the player is completely able to move, and the zombies are able to find the shortest path to reach the player and they have a great walk animation.

I guess a video would demonstrate my progress better than some boring text so:

Next step: Shooting mechanic

EDIT: At the beginning of the jam I said that I'm not sure if I could finish the game within the time limit, but now I feel more confident, it's not that hard actually.