New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes

We use symplectic self-dual additive codes over \begin{document}$ \mathbb{F}_4 $\end{document} obtained from metacirculant graphs to construct, for the first time, \begin{document}$ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $\end{document} qubit codes with parameters \begin{document}$ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $\end{document} . Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.