Push the first sphere (the one you're in) up then right. Wait for the spheres to stop and the gate to close before pushing the same sphere up. Then quickly go down to the sphere beside the gate and push it. There should be three spheres forming an incomplete bridge now and you should now push the final boulder to that bridge and you win.
Now try solving it with a score of 2840. That's what I got
My score at first was 2800, but when I started with the screen still dark I got to 2840, same as you. I don't think it could be done any faster because of waiting for the gate to close.