Let \( P \) and \( Q \) be the points on the line \( \dfrac{x+3}{8} = \dfrac{y-4}{2} = \dfrac{z+1}{2} \) which are at a distance of \( 6 \) units from the point \( R(1, 2, 3) \). If the centroid of the triangle \( PQR \) is \( (\alpha,\beta,\gamma) \), then \( \alpha^{2} + \beta^{2} + \gamma^{2} \) is:
