$\large{\begin{array}{ccccccc} && & & \color{blue}X& \color{blue}X & \color{blue}X&\color{blue}X\\ && & & \color{green}Y& \color{green}Y & \color{green}Y&\color{green}Y\\ +&& & & \color{red}Z& \color{red}Z & \color{red}Z&\color{red}Z\\ \hline & & & \color{green}Y& \color{blue}X& \color{blue}X & \color{blue}X&\color{red}Z\\ \hline \end{array}}$

If $\color{blue}X$, $\color{green}Y$ and $\color{red}Z$ are distinct digits in the sum above, then find $\color{red}Z$.

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