Here is a scale diagram for the D Dorian scale on the C6 neck.  It is for the position in which the root begins on the 10th string, with the scale moving in a right/vertical direction.

This can help in visualizing this particular pocket of the fretboard, and can also help in memorizing the notes of the scale and the fretboard.

You can click on the image (on the attachment page too) to get a better view of the diagram.  Enjoy!