  In this paper we consider some new classical effects obtained for a planar
electrodynamics with the presence of a higher order derivatives term. The model
can be interpreted as a kind of extension for the $3d$ Maxwell-Chern-Simons
electrodynamics with higher order derivatives. We consider setups with
stationary field sources describing point-like charges and Dirac points. We
also investigate this model with the presence of a conducting line (in $3d$
dimensions, it is the equivalent of a conducting plate in $4d$ dimensions). In
this case we calculate the propagator for the gauge field and the interaction
force between the conducting line and a point-like charge, as well as the force
between the conducting line and a Dirac point, the source for vortex field
solutions. It is shown that the image method is not valid in any case. We also
compare the obtained results along the paper with the corresponding ones
obtained with the standard Maxwell-Chern-Simons electrodynamics [1].
