Banjo guitars are odd ducks. I have one with a decent scale length, and the description of your problem seems to be due to the scale length (combined with string gauge). If the scale is short, the strings will be looser and the sound tubby. If the strings are too heavy, the sound will be tubby. If it's a guitar banjo, the sound will be tubby. (Oops! -- actually, most banjo guitars are somewhat tubby sounding, so getting a good bright sound is a little hard.

If the string length is 24" or so, try tuning high a whole tone. If the strings seem too stiff, use lighter gauge and still tune high. If the string length is 25" or so, use lighter strings and tune to standard pitch. As the others have said, be sure to tighten the head well (that 1/4-turn thing is important, since you want to get the brackets all the same around the rim).

And experiment a lot with tension and guage and pitch. Strings are cheap enough to take the time to get the thing right.

Bob Clayton