  In this paper, we introduce PoMiN, a lightweight $N$-body code based on the
post-Minkowskian $N$-body Hamiltonian of Ledvinka et. al., which includes
general relativistic effects up to first order in Newton's constant $G$, and
all orders in the speed of light $c$. PoMiN is written in C and uses a
fourth-order Runge-Kutta integration scheme. PoMiN has also been written to
handle an arbitrary number of particles (both massive and massless), with a
computational complexity that scales as $O(N^2)$. We describe the methods we
used to simplify and organize the Hamiltonian, and the tests we performed
(convergence, conservation, and analytical comparison tests) to validate the
code.

General Relativity and Quantum Cosmology