  Previous work has shown that time-reversal symmetric Weyl semimetals with a
quadrupolar arrangement of first-order Weyl nodes exhibit a mixed
crystalline-electromagnetic response. For systems with higher order Weyl nodes,
which are attached to both surface and hinge Fermi arcs, additional phenomena
appear on surfaces of codimension $n>1$, such as electromagnetic responses of
the hinges. Here we construct a model possessing a quadrupole of higher order
Weyl nodes to study the interplay between higher order topology and mixed
crystalline-electromagnetic responses. We show that the higher order nature of
the Weyl nodes yields a dipole of Dirac nodes on certain surfaces, leading to a
mixed crystalline-electromagnetic \emph{surface} response that binds charge to
dislocations and momentum-density to magnetic fields. In addition, we show that
the model possesses a bulk quadrupole moment of crystal-momentum that provides
a link between the bulk and surface responses of the system.
