Some of the noise would be telegraphed through the ductwork, so nothing you do short of changes would affect that.
One thing often specified but rarely implemented in the ductwork is a flexible coupling between the furnace itself and the remainder of the ductwork. If the ducts are solid, screwed to the top of the furnace, cutting out a section and inserting a properly designed flexible (special coated cloth) section will stop vibrational transmission of sound through the metal.
A second layer of drywall may be the safest. You shouldn't put just some foam panels up, as this room should be fire resistant (and not give off noxious gasses if it did catch fire).
There are a couple of methods to minimize noise transmission through the walls. If you have enough depth, adding another wall so the studs are independent and can't transmit sound through, then insulating it works. Normally, they'd use a 2x6, then put 2x4 studs set so they alternate at the proper spacing, with normal 16" , and attach the drywall to each side. This breaks the transmission path from one side of the stud to the other since they are now separate. The top and bottom plates are the same, though.
There is some special non-hardening, noise damping caulk that can be used to adhere a second layer of drywall to the first. The second layer helps a lot, and the rubbery caulk decouples both layers.
Another possibilty is to use special clips to separate a second layer of drywall, and then anchor it to that creating a second layer.
Seal all joints well.
First thing I'd do, though, is put in the proper isolator in the output duct and see if that's enough.