The locus of lines in $Q$ leading generically to $\mathbb{Z}/2$-numerical Godeaux surfaces (with two fixed double base points of the bicanonical system) is birational to a bundle $Z$ over $\mathbb{P}^3$. The procedures gives two parametrization homomorphisms from $S_a$ to the coordinate ring of $Z$, where the image of each map gives a point in $Q$ whose connecting line is completely contained in $Q$ and leads generically to a $\mathbb{Z}/2$-Godeaux surface.
The object precomputedTorsZ2Line is a method function.