Genial level! What helped me to find out the route before to start pushing, was to visually partition the configuration into locks. From there, I opened one after the other and had the surprise to arrive at target 2 off on first try! I cut the two steps on my 2nd try. A real good one.
Gosh, I had serious problems, here. Just couldn't solve it, always got stuck. Then I somehow reached the exit, but in 50 steps. Two tries more and only then did I get 40. Splendid!