I didn't check all the different gates if a similar design can be found. I made some parts for a round gate with wooden sticks in between some time ago. This is similar, but results in a cube. The size depends only on the wooden sticks (5mm).
V1 is the first try with holes which are exactly 5mm in the design. But my printer makes them smaller.
V3 has some adjustments for my printer to get quite exact 5mm holes.
I chose supports only from the ground plane so that the holes are not filled. Sometimes the roof falls in a bit and I have to drill it to the correct size.