Thats sealed on three sides from your picture. Protect it with lasers and flood lights. Laser beams across the access point on the inside so as soon as they enter the property it triggers an alarm in the house. Flood lights on PIRs.

Also get a camera and stick the monitor by the TV or whereever you spend most your time so you look at it when the flood light comes on. Some wireless cameras have portable monitors so you can even stick it on the bedside cabinet to check in the night if you hear something.

If you are worried about them climbing then razor blades (stainless of course) on the inside top edge of the gate just poking proud of the top. They wont see them so wont expect them until its too late and they grip the gate to pull themselves up, then they will scream like little piggys as it slices into thier hands.