No ,you will not receive new installation code every time you re- install however if you replace your computer or make extensive hardware changes you will receive a new installation code.
Note: You can uninstall and reinstall an activated copy of QuarkXPress on the same computer as many times as you want without reactivating the application.
After activation, QuarkXPress verifies the validity of the activation key each time it is launched. If QuarkXPress fails to detect a valid activation key, you must reactivate the software by contacting Quark customer service, submitting the online form, or faxing the reactivation form.
You must reactivate QuarkXPress if you make a significant hardware change (such as changing the Ethernet address on a Mac® or changing the computer processor) or if the activation mechanism is damaged in some way.