The way I see it. It`s a minor chord. Let me show you why.
A Quartal chord is based in Quartal Harmony instead of Tertian Harmony. That means using intervals of fourth to build chords.
Take a "C Major Scale"
C D E F G A B C D E F
1 2 3 4 5 6 7 8 9 10 11
Now start on the 2nd(D) and add intervals of fourth above it. You get:
DQ=[D,G,C,F]

That "F" at the end defines the chord as a minor.

So, in a common Jazz Progression( ii7-V7-I )
in the key of "C"; that`ll be........( Dm7-G7-C )

Now take a look at the notes of the (Dm7 chord) and the notes in the (DQ chord):
Dm7=[D,F,A,C]
DQ= [D,G,C,F]


You can sustitut the Dm7 and play the jazz progression as fallows:
DQ-G7-C.