Make a Soft-Body to follow path

I am making a small tetris animation but the problem is that the blocks are not falling as they should. Sometimes they collide with the container walls and slow down and sometimes they do not land on the position they need to. I was wondering whether I can make soft bodies follow a path while taking gravity into consideration. If yes, can I make the blocks collide with the container, spin and position them where needed? When I searched for this a bit, I found out that I would have to use soft-body goal and vertex groups but I have no idea how to use them.

So can anyone please explain this to me? Thanks.

Blend file (http://pasteall.org/blend/index.php?id=51918)