Quantum code construction from two classical codes and over the field ( is prime and is an integer) satisfying the dual containing criteria using the Calderbank–Shor–Steane (CSS) framework is well-studied. We show that the generalization of the CSS framework for qubits to qudits yields two different classes of codes, namely, the -linear CSS codes and the well-known -linear CSS codes based on the check matrix-based definition and the coset-based definition of CSS codes over qubits. Our contribution to this article are three-folds. 1) We study the properties of the -linear and -linear CSS codes and demonstrate the tradeoff for designing codes with higher rates or better error detection and correction capability, useful for quantum systems. 2) For -linear CSS codes, we provide the explicit form of the check matrix and show that the minimum distances and are equal to and , respectively, if and only if the code is nondegenerate. 3) We propose two classes of quantum codes obtained from the codes and , where one code is an -linear code ( divides ) and the other code is obtained from a particular subgroup of the stabilizer group of the -linear CSS code. Within each class of codes, we demonstrate the tradeoff between higher rates and better error detection and correction capability.