  We consider a system of weakly coupled Rashba nanowires in the strong
spin-orbit interaction (SOI) regime. The nanowires are arranged into two
tunnel-coupled layers proximitized by a top and bottom superconductor such that
the superconducting phase difference between them is $\pi$. We show that in
such a system strong electron-electron interactions can stabilize a helical
topological superconducting phase hosting Kramers partners of $\mathbb{Z}_{2m}$
parafermion edge modes, where $m$ is an odd integer determined by the position
of the chemical potential. Furthermore, upon turning on a weak in-plane
magnetic field, the system is driven into a second-order topological
superconducting phase hosting zero-energy $\mathbb{Z}_{2m}$ parafermion bound
states localized at two opposite corners of a rectangular sample. As a special
case, zero-energy Majorana corner states emerge in the non-interacting limit
$m=1$, where the chemical potential is tuned to the SOI energy of the single
nanowires.
