You have to start with something like an SVG file, rather than a bitmap (JPG, PNG, etc.) in order to create an extrusion. You can use Inkscape (free) to do a bitmap trace of the image, creating an SVG file. With the SVG file, the easiest program to use is Tinkercad, which allows you to Import the file, then set the desired height. You can add a backing to the shape and export as STL in order to 3D print. Depending on the size you intend to print, the thin lines in the middle will not print well. It may be necessary to make thicker the outer perimeters as well.

There are other programs which will accomplish the same results, but are slightly more difficult to learn than Tinkercad. All of them will require to begin with an SVG or similar vector file, not a bitmap.