The QXD file extension is linked to the QuarkXPress Document Format. QuarkXPress is a desktop publishing software used primarily by printers, publishers, and advertising agencies to design and print publications, catalogs, and other high-quality print products.
QXD is a proprietary format that can only be opened and edited with QuarkXPress and Adobe InDesign (using the Markzware plugin). The QXD format includes texts and layout instructions, but not images and fonts. These must be supplied separately to get everything displayed correctly.
If you do not have access to one of the programs, you should ask the creator to export the QXD file as a pdf or eps file. These file formats can be imported into many more (even free) programs and continue to edit.
It should also be noted that Quark's QXD format was changed to version 6.0 and replaced with qxp. However, Qxd files can be read in a newer version of quarkXPress.