  We compute the holographic stress tensor and the logarithmic energy-momentum
tensor of Einstein-Weyl gravity at the critical point. This computation is
carried out performing a holographic expansion in a bulk action supplemented by
the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined
by the addition of this topological term has the remarkable feature that all
Einstein modes are identically cancelled both from the action and its
variation. Thus, what remains comes from a nonvanishing Bach tensor, which
accounts for non-Einstein modes associated to logarithmic terms which appear in
the expansion of the metric. In particular, we compute the holographic
$1$-point functions for a generic boundary geometric source.
