The locus of lines in $Q$ leading generically to $\mathbb{Z}/4$-numerical Godeaux surfaces (with two fixed double base points of the bicanonical system) is birational to a union $\mathbb{P}^3 \ times \ \mathbb{P}^1$. The procedures gives two parametrization homomorphisms from $S_a$ to the coordinate ring of a $\mathbb{P}^3 \ \times \ \mathbb{P}^1$, where the image of each map gives a point in $Q$ whose connecting line is completely contained in $Q$ and leads generically to a $\mathbb{Z}/4$-Godeaux surface.
The object precomputedTorsZ4Line is a method function.