In ths paper we study the VOA \(V_{\mathcal{J},r}\) constructed by Ashihara and Miyamoto, We construct simple quotients of \(V_{\mathcal{J},r},r\in\mathbb{Z}_{\neq 0}\) explicitly using dual-pair type constructions. We also compute the character formula of the simple quotients when \(r=-2n,n\geq 1\).