No picket fences.

I was going to put a nice picket fence around the mutfruit field at Country Crossing, but when I open the workshop, fences menu, there aren't any picket fences! I have junk fences, wire fences, and chain link, but no picket.

I have three copies of the magazine, still nothing.

Anyone know how to fix this?

You might not have the right Picket Fences magazine. Each one gives certain items to build.

The correct one can be found in

according to the wiki.

If you want more details on locations of the magazines you could go http://fallout.wikia.com/wiki/Picket_Fences.