Abstract: The concept of complex-rotary codes of genusg=1 is proposed in this paper. By means of the complete embedding of multi-layer ring surfaces, a visual model of GICR codes is given. The codes are the extension of complex-rotary codes from 2- dimensional space to 3-dimensional space. By using the conception of the weak block design, the minimum distance and error-correcting capability of the codes are discussed. Meanwhile, the dual codes of GICR codes are studied, and the main parameters of GICR codes and their dual codes are also presented.