This challenge is part of Fortnite Season 3 Week 6 Challenges and you'll have to fish a weapon at Stack Shack. This strange place is a tiny islet located in the far west of the map. Strictly speaking, it's only a small shed on a rock.
Map
"Catch" a weapon actually means "fish" a weapon. You'll have to find a fishing rod or harpoon and then try your luck on one of the schools of fish nearby.
The good news is that a fishing rod barrel is accessible directly from the shed. It's possible to land on the spot and start fishing immediately. Please note that this place will be very popular at the time the challenge is released. The safest way to do this is to land in a nearby town or city and then go to Stack Shack later in the game.
Grey weapons can also be fished out of schools of fish in "normal" waters. Also, don't panic if there are no schools of fish near Stack Shack: you'll always be able to complete the challenge with a rod.
Original content by Romain "Zorg" Becquelin.