The number of bipolar orthogonal codes such as Walsh-Hadamard (WH) is limited due to implementation complexity which is proportional to the number of generated codes. Therefore, the data rate of multi-code systems [1] is restricted too. This paper presents a design of novel multi-level quasi-orthogonal codes (MLQOCs) using advanced orthogonal code group (AOCG) [2] derived from WH matrix to provide more spreading codes while retaining the chip-rate and length of the original WH codes. Moreover, we propose a multi-code multi-carrier CDMA (Mc-MC CDMA) system using MLQOCs to obtain high and variable transmission speed.