Upper-bound conjecture for lines on Weddle surfaces

Let $Z$ be a set of six points in linearly general position in $\mathbb{P}^3$, and let $\mathcal W(Z)$ denote its Weddle surface. Upper-bound conjecture for lines on Weddle surfaces. The surface $\mathcal W(Z)$ contains at most $37$ lines. This is motivated by the example in the paper producing $37$ lines and by comparison with known bounds for lines on smooth and nodal quartic surfaces; the supplied text does not establish the proposed upper bound.