Examples of rank two ACM bundles on smooth quartic surfaces in $\mathbb{P}^3$

Let $ F \subseteq \mathbb{P}^3 $ be a smooth quartic surface and let $ \mathcal{O}_F(h):=\mathcal{O}_{\mathbb{P}^3}(1) \otimes \mathcal{O}_F$. In the present paper we classify locally free sheaves $\mathcal{E}$ of rank 2 on $F$ such that $ c_1(\mathcal{E})=\mathcal{O}_F(2h),c_2(\mathcal{E})=8 $ and $ h^1(F,\mathcal{E}(th))=0$ for $t \in \mathbb{Z}$. We also deal with their stability.