I have to search the crate in the lumber yard, but i cannot get in because when i try to go through the fence it says "I don't want to snag my clothes".

I'm pretty sure you have to either start Gertrude's Cat(or something similar to that) quest, or finish it.

 

 

 

I think.

Right near the middle of the southern fence there's a spot you can "climb-over fence". It looks like a gate (a red line) on your mini-map. If you've tried that and it still won't let you over, then yup, you need to start Gertrude's Cat.

 

 

 

 

 

 

 

You don't have to finish the quest if you don't want to. You only need to do up to the part where you speak to either Shilop or Wilough in Varrock Square Market. Once you pay them 100gp and they tell you that their secret playground is at the lumberyard, you will be able to enter the lumberyard.

 

 

 

 

 

 

 

But if you go through the trouble of doing that, you may as well finish the quest. You'll need a cat for the Icthlarin's Little Helper quest anyway.