Existence of non-hyperplanar $(q^2+q+1)$-ovoids of the parabolic quadric

Let $q$ be a prime power greater than $2$, and let $\mathcal{Q}(8,q)$ be the parabolic quadric in projective $8$-space. An $(q^2+q+1)$-ovoid is a set of points meeting every generator of $\mathcal{Q}(8,q)$ in exactly $q^2+q+1$ points. Non-hyperplanar ovoid conjecture. There exists a $(q^2+q+1)$-ovoid of $\mathcal{Q}(8,q)$ which is not contained in a hyperplane for every prime power $q>2$. The claim is verified computationally for $q=3,4,5$; the case $q=2$ is excluded because the computed example is an embedded $\mathcal{Q}^-(7,q)$. Existence for all larger prime powers remains open.