The six faces of a cubical die are numbered with $$2^{0},2^{1},2^{2},2^{3},2^{4},2^{5}$$ in such a way that the product of the numbers on any pair of opposite faces is $$2^{5}$$. Two such dice are stacked one on top of another. If $$𝑁$$ is the greatest possible sum of the $$9$$ visible numbers (for all such arrangements of dice), find the sum of the squares of the digits of $$𝑁$$.