Minor 7th chords (m7)
Dm → Dm7
That way a Dm changes into a Dm7.
To generate a seventh by raising the fifth makes not much sense here.
Dm7 as barre chord
I'd recommend to play the Dm7 as barre chord. At the fifth (V.) fret you'll find a shape equivalent to the Am7 we talked about before.
Here you can again (like before with Em7 and Am7) replace the fifth on the high E-string by the seventh located three frets higher.
Move that chord shape along the guitars fretboard to obtain other minor 7th chords, like e.g. Cm7 (two frets lower), Ebm7 (one fret higher), etc.
Gm → Gm7
You can treat the Gm barre chord exactly like the Em discussed in the beginning - just three frets higher at the III.fret.
Here as an example the Gm7 chord including the seventh two times. That sounds great and is handy to play.
Further chord shapes
There are quite a few different chord shapes for minor 7th chords. The root does not always have to be the lowest note, for instance if you've got a second instrument (bass, piano,...) playing the bass note, or if you're packing more than one chord shape of the same chord into a bar to make your accompaniment more interesting.
This lesson is not intended for showing all possibilities. The construction of minor seventh chords should be clear by now. The chord finder shows more m7 chord shapes - you can also fiddle out others by yourself with the help of the analyzer function!