  We prove that an additive form of degree $d=2m$, $m$ odd, $m\ge3$, over the
unramified quadratic extension $\mathbb{Q}_2(\sqrt{5})$ has a nontrivial zero
if the number of variables $s$ satisifies $s \ge 4d+1$. If $3 \nmid d$, then
there exists a nontrivial zero if $s \ge \frac{3}{2}d + 1$, this bound being
optimal. We give examples of forms in $3d$ variables without a nontrivial zero
in case that $3 \mid d$.
