Double check that the gate is locked. And, as Danielle mentioned, where are the zombies appearing? They have spawning points and they will always come out of those spots. If you have built the fence around a spawning spot, the zombies are already inside the fenced area and there's nothing you can do. Make sure you put your garden and fence away from the spawning spots. Also, do you have the peashooters? I think the came as an additional piece to Supernatural, but they will shoot the zombies when they appear.