Let the image of the point \( P(1, 2, 6) \) in the plane passing through the points \( A(1, 2, 0) \), \( B(1, 4, 1) \) and \( C(0, 5, 1) \) be \( Q(\alpha, \beta, \gamma) \). Then \( \left( \alpha^{2} + \beta^{2} + \gamma^{2} \right) \) is equal to:
\( 76 \)
\( 62 \)
\( 65 \)
\( 70 \)
