After a brief review of the general presymplectic AKSZ approach we apply it to conformal gravity. More specifically we identify a compatible presymplectic structure on the minimal model of the total BRST complex of the theory. Together with the BRST differential this structures determine a full-scale BV formulation for a specific frame-like action which seems to be not known before. Remarkably, the underlying frame-like description does not require any artificial off-shell constraints. Instead, the action becomes equivalent to the usual conformal gravity one upon gauging away all the pure gauge variables associated to the kernel of the symplectic structure.