  We present an exploratory investigation of the parity odd $\Delta I = 1$
pion-nucleon coupling $h_\pi^1$ from lattice QCD. Based on the PCAC relation,
we study the parity-conserving effective Hamiltonian and extract the coupling
by determining the nucleon mass splitting arising from the effective 4-quark
interactions using the Feynman-Hellmann theorem. We present preliminary results
of the mass shift for a $32^3 \times 64$ ensemble of $N_f = 2 + 1 + 1$ twisted
mass fermions at pion mass $260$ MeV and lattice spacing $a = 0.097$ fm.
