  We study the non-equilibrium transport properties of a highly anisotropic
two-dimensional lattice of spin-1/2 particles governed by a Heisenberg XXZ
Hamiltonian. The anisotropy of the lattice allows us to approximate the system
at finite temperature as an array of incoherently coupled one-dimensional
chains. We show that in the regime of strong intrachain interactions, the weak
interchain coupling considerably boosts spin transport in the driven system.
Interestingly, we show that this enhancement increases with the length of the
chains, which is related to superdiffusive spin transport. We describe the
mechanism behind this effect, compare it to a similar phenomenon in single
chains induced by dephasing, and explain why the former is much stronger.
