  We propose a method to compute the Wilson coefficients of the weak effective
Hamiltonian to all orders in the strong coupling constant using Lattice QCD
simulations. We perform our calculations adopting an unphysically light weak
boson mass of around $2~\mathrm{GeV}$. We demonstrate that systematic errors
for the Wilson coefficients $C_1$ and $C_2$, related to the current-current
four-quark operators, can be controlled and present a path towards precise
determinations in subsequent works.
