дверь is a single door as a subject. двери can be a single door when using a negative sentence like "there is no door here" здесь нет двери. Both are single door but the case is different. In this example, it is a positive subject so we need the nominative дверь. At least this is what i understand.
It's grammatically plural, but «две́ри» can mean a single door (especially if it's a double-leaf door), so I believe "The door is far away" should be accepted too.