Let $\overrightarrow{a}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}, \overrightarrow{b}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}-2\hat{\mathrm{k}}$ and $\overrightarrow{c}=-\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}.$ If $\overrightarrow{d}$ is a vector perpendicular to both $\overrightarrow{\mathit{b}}$ and $\overrightarrow{c},$ and $\overrightarrow{\mathit{a}}\mathit{·}\overrightarrow{\mathit{d}}=18,$ then $|\overrightarrow{a}\times \overrightarrow{d}{|}^2$ is equal to