Construction X is known from the theory of classical error control codes. We present a variant of this construction that produces binary stabilizer quantum error control codes from arbitrary quaternary linear codes. Our construction does not require the classical linear code C that is used as the ingredient to satisfy the dual containment condition, or, equivalently, C^\perp_h is not required to satisfy the self-orthogonality condition. We prove lower bounds on the minimum distance of quantum codes obtained from our construction. We give examples of record breaking quantum codes produced from our construction when C is nearly dual containing, or, equivalently, C^\perp_h is nearly self-orthogonal.

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