Click the second color stop from the left—the dark magenta one—to select it. (I know, the swatch looks purple, but if you go by the Hue value, it’s magenta. I guess I’m a stickler.) Two options, Color and Location, become available at the bottom of the dialog box. Click the Color swatch if you want to change the color; modify the Location value or drag the color stop to move the color in the gradient. Increasing the Location value darkens the colors in the image; reducing the value lightens them. (This isn’t always the case—it depends on the colors in your gradient—but that’s how it works in this gradient.)
I recommend that you reduce the Location value for the dark magenta color stop to 15 percent. Then click the next color stop over—the dull red one—and change its Location to 35 percent. Both changes lighten the image incrementally, just as if you moved points on the brightness graph inside the Curves dialog box.
Enter “Quadtone Modified” into the Name option box and click the New button to add a swatch to the end of the Presets list.

Click OK to accept your changes and return to the Gradient Map dialog box.
Assuming the Preview check box is on (as by default), Photoshop will apply the colors in this gradient to the luminosity values in the image. The gradient we used progresses from black to very dark magenta followed by a dull red, orange, and finally white, each of which finds a home over the course of the gray values in the photograph, as shown below. That’s a total of four colors plus white, hence a quadtone. (If your image still appears black and white, it’s because you didn’t convert the image from grayscale to RGB, as explained in Step 2.)

To see what other gradients look like when applied to your grayscale image, click the arrow to the right of the gradient bar and select a different gradient swatch. The image below illustrates one of Photoshop’s default gradients, Copper. I turned on the Reverse check box, which reverses the order of the colors in the gradient and inverts the colors in the image.

Copper Reverse
Once you arrive at a favorite, click the OK button or press the Enter or Return key to accept the colorized image. (If the gradient swatch panel is visible, you may have to press Enter or Return twice.)
You can, of course, apply more colorful gradients to an image. But the more you vary the colors, the more psychedelic and convoluted your colorized image becomes. I advise subtle changes. Even small shifts in color can make a big difference.