Brilli the Ant is Brilliant! Part 2

Brilli the ant, is on the 3-dimensional plane. He is standing on $(0,0,0)$ . It takes him $2$ minutes to crawl one unit. The probability that Brilli is crawls to $(2,2,2)$ can be written as $\frac{m}{n}$ . Find $m+n$

Notes and Assumptions: Brilli only moves forwards and backwards, left and right, and Brilli also moves up and down.