Let $$A, B,$$ and $$C$$ be 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 $$\triangle ABC$$ be a  conic $$C_0$$, then three times the length  of latus rectum of  $$C_0)$$ is :