I agree with getting a more powerful filter. Goldfish are really messy fish. We have two aquariums and the one that has the goldfish is a 30 gallon with a 65 gallon filter and crayfish to keep the bottom clean. You don't have to go that over the top (maybe a 25 gallon filter? )
but to give an idea, the tank we keep them in was already cycled from when we kept African cichlids ( who love to dig and make a dirty tank) and the water slowly became murky. Now it's crystal clear with the more powerful filter.