The Mendix Mobile app (using the QR code functionality) unfortunately does not support push notifications. The required Phonegap plugin is not included in the app due to security concerns (because of the nature of the Mendix Mobile app, which is designed to open and run any number of Mendix apps).
In order to use push notifications, please build a mobile package (Android or iOS) for your Mendix app using e.g. Phonegap Build, as described on https://docs.mendix.com/howto/mobile/publishing-a-mendix-hybrid-mobile-app-in-mobile-app-stores. If you're targeting Android, then you only need steps 1 through 3 during development.