  We use a Diamond diagram attached to a $2$-dimensional reducible split mod
$p$ Galois representation of
$\mathrm{Gal}(\overline{\mathbb{Q}_{p}}/\mathbb{Q}_{p^{2}})$ to construct a
non-admissible smooth irreducible mod $p$ representation of
$GL_{2}(\mathbb{Q}_{p^{2}})$ following the approach of Daniel Le.
