An example of menu is the inventory menu (the pause menu). You can download any project made by Christopho and study these scripts.
Doors do not have collision tests or events like "on_interaction" or "on_activated", so you should use other entity to detect the interaction somehow and then start the menu. So you really need 2 entities, the door, and other entity to detect the interaction (and you can start the menu when there is interaction with this entity, defining that interactin event from the map script, which would start you menu and initialize it with the particular info).
(Sorry if I don't give more explanations, I am a bit busy. But I'm sure others can help you more if my hints are not enough for you.)