If you want something more neutral to allow the red of the brick to be the focal point of color, you will want to stick with a darker neutral. "Deep charcoals such as Iron Ore SW 7069 or Sealskin SW ...
For example, a Lounge Green door in the middle of a brick facade will pull focus in the best way. BEHR's Underwater shade is a stormy sea blue that leans gray. It's colorful without being too vibrant ...