  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.
