The Dorian sharp 4 mode can be used for any minor triad or a 6th, 7th, 9th or 11th. A very useful mode.
A point to remember about chords. A major 6th is also a minor 7th chord.
An example F-A-C-D is an F6 chord and D-F-A-C is a Dm7.
This means that you can use this scale over an F6 chord too. This will depend on the song and what sound you want.
This theory will work well sometimes not so well other times. When you see an F6 they usually want a F bass note not a D and vice versa.
Experience will tell you when to use it and when not to. Experiment.
Here are a few Dm7 chord forms.
Here is what this dorian sharp 4 mode sounds like played against a Dm7 chord.
The D Dorian sharp four play against a D minor 7th chord
It’s like a minor pentatonic with one of the blue notes(♯4/♭5) in it.
The Dorian ♯4 Mode List
The Dorian ♯4 Mode Formula
Raise the 4 of the Dorian by one fret.
Here it is based on the major scale.