The capacity of a wireless lattice network with local interference is studied. In particular, the transport capacity under a multiple unicast traffic pattern is studied for a network of nodes placed on the hexagonal lattice. The communication model is that local interference allows reliable broadcast to all neighbors, but that simultaneous transmissions from multiple neighbors lead to a collision. If broadcast is not exploited and only point-to-point transmissions are used, the normalized transport capacity was previously shown to be between 1/3 and 2/5. In this work it is demonstrated that by exploiting broadcast the normalized transport capacity of the hexagonal lattice is at least 3/7.