Jacobian ideal containment conjecture for points in general linear position

Let $\mathbb X\subseteq \mathbb P^2$ be a set of $s=\binom{d+1}{2}$ points in general linear position, and let $I$ be the Jacobian ideal of $I(\mathbb X)$. Jacobian ideal containment conjecture. If $d\geq 6$, then

$$(x,y,z)^{2d-2}\subseteq I.$$

This extends the preceding verified cases $d=4,5$ and predicts the indicated containment for all larger values of $d$; the source provides no resolution of the claim.