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We present a family of non-CSS quantum stabilizer codes using the structureof duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantumcodes can possess varying dimensions, and their minimum distances are boundedby a square root bound. For each fixed dimension, this allows us to constructan infinite sequence of binary quantum codes with a growing minimum distance.Additionally, we demonstrate that this quantum family includes an infinitesubclass of degenerate codes with the mentioned properties. We also introduce atechnique for extending splittings of duadic constacyclic codes, providing newinsights into the minimum distance and minimum odd-like weight of specificduadic constacyclic codes. Finally, we establish that many best-known quantumcodes belong to this family and provide numerical examples of quantum codeswith short lengths within this family.

Infinite class of quantum codes derived from duadic constacyclic codes