Let \( ABC \) be a triangle of area \( 15\sqrt{2} \) and the vectors \( \overrightarrow{AB} = \hat{i} + 2\hat{j} - 7\hat{k} \), \( \overrightarrow{BC} = a\hat{i} + b\hat{j} + c\hat{k} \) and \( \overrightarrow{AC} = 6\hat{i} + d\hat{j} - 2\hat{k},\ d > 0 \). Then the square of the length of the largest side of the triangle \( ABC \) is \( \_\_\_\_\_\_\_\_\_\_ \).
