Hyperbolic groups containing subgroups of type ${\mathcal{F}}_3$ not ${\mathcal{F}}_4$

We give examples of hyperbolic groups which contain subgroups that are of type ${\mathcal{F}}_3$ but not of type ${\mathcal{F}}_4$. These groups are obtained by Dehn filling starting from a non-uniform lattice in $\mathrm{P}\mathrm{O}(8,1)$ which was previously studied by Italiano, Martelli and Migliorini.