To accomplish relatively complex tasks, in Internet of Bio-Nano Things (IoBNT), information collected by different nano-machines (NMs) is usually sent via multiple-access channels to fusion centers (FCs) for further processing. Relying on two types of molecules, in this paper, a molecular code-division multiple-access (MoCDMA) scheme is designed for multiple NMs to simultaneously send information to an access-point (AP) in a diffusive molecular communications (DMC) environment. We assume that different NMs may have different distances from AP, which generates `near-far' effect. Correspondingly, the uniform and channel-inverse based molecular emission schemes are proposed for NMs to emit information molecules. To facilitate the design of different signal detection schemes, the received signals by AP are represented in different forms. Specifically, by considering the limited computational power of nano-machines, three low-complexity detectors are designed in the principles of matched-filtering (MF), zero-forcing (ZF), and minimum mean-square error (MMSE). The noise characteristics in MoCDMA systems and the complexity of various detection schemes are analyzed. The error performance of the MoCDMA systems with various molecular emission and detection schemes is demonstrated and compared. Our studies and performance results demonstrate that MoCDMA constitutes a promising scheme for supporting multiple-access transmission in DMC, while the channel-inverse based transmission can ensure the fairness of communication qualities (FoCQ) among different NMs. Furthermore, different detection schemes may be implemented to attain a good trade-off between implementation complexity and communication reliability.