27MHz AM was all there was in DK when I was a teen and there were some serious gear produced then.
I don't really believe that it should be as bad as 20' and with what have been tested, I would consider a slightly defect transmitter or receiver, as I assume you're supposed to control an airplane with it (so I'd guess on at least a 300' to 500' range).
I just found a manual for the 2E and 2F version of their 27MHz AM and here is a passage from that, under the heading "Performance Test and Mounting Precautions":
Make [transmitter] antenna as short as possible (in the case of FP-T2F, extend one section of the antenna) and extend the receiver antenna [fully] and attempt operation from a distance of 20m~30m [60' to 90']. Operation is normal if all the controls are functioning properly. Perform this test within a maximum of 5 minutes time. Never perform this test when the transmitter antenna is not mounted to the transmitter. Otherwise the transmitter will be adversely affected.
This tells us that even with the antenna down it should have a much larger range than 20', so clearly, either TX or RX is bad.
Bring it back to whoever sold you the set for a replacement.