Let \( A \), \( B \) and \( C \) be the vertices of a variable right angled triangle inscribed in the parabola \( y^2 = 16x \). Let the vertex \( B \) containing the right angle be \( (4, 8) \) and the locus of the centroid of \( \Delta ABC \) be a conic \( C_0 \). Then three times the length of latus rectum of \( C_0 \) is ________.
