We develop quantum weighted algebraic geometry (QWAG) codes: CSS codes obtained from evaluation codes on quasi-smooth hypersurfaces in weighted projective planes \(\mathbb {P}(w_0,w_1,w_2)\) over finite fields. A single quasi-smooth weighted-homogeneous equation realizes curves of genera with no smooth plane model with \(\deg (H|_X)\) and \(\deg (K_X)=2g-2\) read off the weights and degree and with an explicit monomial Riemann–Roch basis whose order-domain structure keeps the codes explicitly encodable and decodable. The weighted adjunction formula renders the CSS self-orthogonality condition \(2G \le K_X + D\) the transparent numerical inequality \(2\deg (G)\le (2g-2)+n\) , yielding broad families of dual-containing codes without ad hoc search. We prove an achievability bound \(d \ge \tfrac{n-k_Q}{2}+1-g\) via residue duality, placing these stabilizer codes within g of the quantum Singleton value, and we record that weighted spaces give no automatic gain in rational points. We further pose, with a supporting orbifold Riemann–Roch heuristic, a conjectural orbifold refinement \(d \le \tfrac{n-k_Q}{2}+1-\tfrac{\epsilon }{2}\) of the converse, where \(\epsilon \) is the total orbifold defect. Since the underlying superelliptic curves are indexed by binary-form invariants—themselves coordinates on a weighted projective moduli space—the framework connects naturally to invariant databases and graded learning architectures as tools for code search and for probing the refined conjecture.
