To obtain the Brentwood Waste Key in Dead Island 2, travel to the western side of Beverly Hills to find the Brentwood Staff on the street in front of the house.
Take him out then loot the Brentwood Waste Key. Now that you have the key, head to the basement of the nearby house to find the Brentwood Waste Bin.
Unlock this bin to find the Puncturator Heavy Wrench.