Wayne is correct, but you need to make sure that the unit is not drawing air through the door to function before sealing it off.
I assume this is in your basement and usually the returns are upstairs - if that is the case, you are gold! If not, you are in a world of hurt!
It is a little ghetto, but you can cut carpet to fit your door and tack it to the inside which would work on your current door and a solid core (depends on how much noise you have and how much you want to get rid of as much as possible).
From a cost approach, I would seal around the doorframe, buy a door transom (or - ghetto option - simply cut a 2X2 to length and caulk it to the floor with construction adhesive and seal as you did around door frame). Now you should have all air gaps sealed so noise must go through the door. See what you have.
If you want to try the scrap carpet, tack it. The door frame will be a solid frame at least 1 " around the outside to place nails. See if it is acceptable!
The solid door will be your greatest cost and you can use the carpet on it if you have cut it to size.
On the other hand a solid core door is cheap compared to what you likely have invested in your system.
If you are hearing mostly blower noise, sealing around the edges will do lots of good. If it is lower frequency motor noise, hum, resonance through ductwork, the solid core door is of greater benefit.
Last, if it is duct resonance, ask your hvac guy about installing insulation inside the duct near the fan. This will often make a big difference. It is a fiberboard type material used for this insulation since fiberglass would fray and be in your air system.
