To answer this question we should surely try to figure out what the mind IS, right? Does the mind actually have any physical properties? As a concept, we know that the mind exists. So by its conceptual existence it must take up space, in the fact that it's considered if nothing else. Possibly another question whose answer could provide insight onto this question is what is the difference between consciousness and the concept of the mind? Is there a difference? I usually consider the mind just a vehicle for consciousness to have a way to be channeled, I suppose. Consciousness is what makes it possible for us to think in the way we do.

The ideas that come from the mind, when somehow manifested physically - like spoken words, art, written word, doing something even - occupy space. These things, which are direct products of the mind and therefore a representation of the mind itself, occupy space. The mind could occupy space as a result of its ideas occupying space. The mind is where thoughts live, so when a thought is successfully translated from some immaterial realm inside one's head to some sort of existence that is tangible, and physical, isn't that the mind occupying a space?

A Different Age by Current Joys
https://www.youtube.com/playlist?list=PLL_4tI1HgJsQU-knBuua8jvzh-wOk9Uy5