  We show theoretically that a heterostructure of monolayer FeTe$_{1-x}$Se$_x$
- a superconducting quantum spin Hall material - with a monolayer of FeTe - a
bicollinear antiferromagnet - realizes a higher order topological
superconductor phase characterized by emergent Majorana zero modes pinned to
the sample corners. We provide a minimal effective model for this system,
analyze the origin of higher order topology, and fully characterize the
topological phase diagram. Despite the conventional s-wave pairing, we find
rather surprising emergence of a novel topological nodal superconductor in the
phase diagram. Featured by edge-dependent Majorana flat bands, the topological
nodal phase is protected by an antiferromagnetic chiral symmetry. We also
discuss the experimental feasibility, the estimation of realistic model
parameters, and the robustness of the Majorana corner modes against magnetic
disorder. Our work provides a new experimentally feasible high-temperature
platform for both higher order topology and non-Abelian Majorana physics.
