Self-dual codes over F5 and s-extremal unimodular lattices

New s-extremal extremal unimodular lattices in dimensions 38, 40, 42 and 44 are constructed from self-dual codes over ${\mathbb{F}}_5$ by Construction A. In the process of constructing these codes, we obtain a self-dual $44,22,14]$ code over ${\mathbb{F}}_5$. In addition, the code implies a $43,22,13]$ code over ${\mathbb{F}}_5$. These codes have larger minimum weights than the previously known $44,22]$ codes and $43,22]$ codes, respectively.