We consider the problem of code constructions for reliable multicast communications over wireless networks with AWGN noise, at rates "near" capacity. We adapt the constructions of Avestimehr-Diggavi-Tse (ADT) to obtain computationally efficient codes that operate at rates that are at most a constant gap from the capacity of the corresponding network. Our primary result shows that concatenation of the quantize-and-map codes proposed by ADT result in block codes which are still at most a constant gap from capacity, but are also computationally tractable to both encode and decode.