In this article, the zonotopic distributed fusion estimation problem is investigated for a class of general nonlinear systems over binary sensor networks subject to unknown-but-bounded (UBB) noises. The network communication from nodes to the fusion center is confined to the limited bit rate. To alleviate the impact from less measurement information of the binary sensor, a modified innovation is constructed to improve the estimation accuracy. Then, a novel coding-decoding approach is proposed to ensure that the decoder has the ability to decode information from each node. Based on the matrix weighting fusion method, a distributed fusion algorithm is put forward under the zonotopic set-membership filtering framework, and the F-radius of the local zonotopic sets are derived and minimized by selecting the filtering gain parameters. Moreover, the bit rate allocation scheme and the weighting coefficients are determined by resolving two optimization problems. In addition, a sufficient condition is established to guarantee the uniform boundedness of the F-radius of the fused zonopotic. Finally, the ballistic object tracking systems is utilized to illustrate the availability of the presented algorithm.