I agree, a 20 minute walk for a Beagle isn't nearly enough exercise. That is a hunting dog who can go for hours. You need to find him another outlet for his energy, like lots of rough and tumble play outside, letting him run in a fenced area, stuff like that.
The other thing is- crate him! A dog will never damage your house if he's crated when you are not around. Our pug is almost 4 and still stays in his crate at night. He will go there to get away from the other dogs, it's his private little place. Our GSD pup is 8 months, he's never eaten anything because he's supervised and if he can't be with one of us, he's crated. The only one we don't crate is our 12 year old but she was crated for about 3 years because she'd chew stuff like table legs.