Generalized Brunella's conjecture for foliations with ample determinant of the normal bundle

Let $X$ be a compact connected complex manifold of dimension $n\geq 3$, and let ${\mathscr{F}}$ be a holomorphic foliation of codimension $r<n$ on $X$. Suppose that the determinant $\det(N{\mathscr{F}})$ is ample.

Generalized Brunella's conjecture. If $n\geq 2r+1$, then every leaf of ${\mathscr{F}}$ accumulates to the singular set ${\rm Sing}({\mathscr{F}})$.

This extends Brunella's codimension-one question to higher-codimension foliations. The source attributes the natural conjecture to Camacho--Perrone and indicates that the codimension-one case is known in the projective cyclic-Picard setting; the generalized statement remains open.