Let the line $L$ be the projection of the line $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-4}{2}$ in the plane $x-2 y-z=3$. If $d$ is the distance of the point $(0,0,6)$ from $L$, then $d^2$ is equal to $\_\_\_\_$ .
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