**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 $x^2$.