A crude drawing but it should work. Only downside is the the crowd will retract after the door goes down. If you want that to be reversed then just switch the relief valve and check valve directions on the rod end of the cylinders to make the sequence that the door opens first and closes last.
As drawn the door opens first and closes first. The pressure reliefs would be set just a tad higher pressure than is required to operate the Gate reliebly, but also under system pressure.
I'm not sure what is all available in the small hydraulic valves and such, so hopefully there is something you can fit in.