  A minimum storage regenerating (MSR) subspace family of $\mathbb{F}_q^{2m}$
is a set $\mathcal{S}$ of $m$-spaces in $\mathbb{F}_q^{2m}$ such that for any
$m$-space $S$ in $\mathcal{S}$ there exists an element in $\mathrm{PGL}(2m, q)$
which maps $S$ to a complement and fixes $\mathcal{S} \setminus \{ S \}$
pointwise. We show that an MSR subspace family of $2$-spaces in
$\mathbb{F}_q^4$ has at most size $6$ with equality if and only if it is a
particular subset of a Segre variety. This implies that an $(n, n-2, 4)$-MSR
code has $n \leq 9$.
