Minimal Reversible Nonsymmetric Rings

Marks showed that $\mathbb{F}_2Q_8$, the $\mathbb{F}_2$ group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256. Furthermore, it is shown that although $\mathbb{F}_2Q_8$ is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo.