Consider the following Miracle Octat Generator or MOG. Choose the sign $\pm 3$ and fill in the blanks $\pm 1$ to create a point $x$ in the Leech lattice $\Lambda_{24}$ with $||x||^2=8$.
$ \frac{1}{2} \begin{array}{|cc|cc|cc|} \hline & & 1 & & \pm 3 & \\ & 1 & & 1 & & \\ \hline & & 1 & & & \\ & & & 1 & & \\ \hline \end{array} $
Not quite sure how to approach the problem. Not looking for an answer, but a sense of direction would be greatly appreciated.