Three Dimensional Geometry: JEE Main 2024 Mathematics question

A line with direction ratios $2,1,2$ meets the lines $x=y+2=z$ and $x+2=2 y=2 z$ respectively at the points $\mathrm{P}$ and $\mathrm{Q}$. If the length of the perpendicular from the point $(1,2,12)$ to the line $\mathrm{PQ}$ is $l$, then $l^2$ is __________.