Radical 3-subgroups of F4(q) with q even

In a recent paper, An and Huang classified the radical 3-subgroups of F4(q) for q odd. Here we use a similar approach to classify the radical 3-subgroups of F4(q) with q even. As an application, we determine the essential rank of the Frobenius category FD(F4(q)) for q even, where D is a Sylow 3-subgroup of F4(q).