past vs across vs through

Literally, you can't pass, pass through, or cross a fence. You can only go over it.

However, in regards to your question, the best word to use is "past".

For example, "I got past the fence" or "I went past the fence".

If I am on a footpath and I pass/go past a fence, it may be parallel to the path or it may stop before reaching the path.

I go/pass through the fence if I go through a hole, perhaps separating the wires of a wire fence. Depending on centext I might go through the fence using a gate, or it may be in cotrast to using a gate.

I go/pass across the fence by climbing across it or by using a stile. Either way "over" is better than "across".