Brilli The Ant is Back!

A 12 feet high room is 40 feet long and 10 feet wide. Brilli the ant is standing in the middle of one of the walls (which is 10 by 12 feet), such that it is 1 foot above the floor, and is equidistant from the other 2 edges of that wall.

In the middle of the wall opposite to Brilli's, rests a sugar crystal, 1 foot below the ceiling. The minimum distance Brilli needs to cover to reach the sugar crystal, assuming that Brilli can walk anywhere inside the room, is $x$. Determine the value of $x^2$.

Image credit: Flickr Snap