Let Y_H≃Σ^{-7} RP^2∧CP^2∧HP^2 be a type 1 spectrum with 8 cells. In this talk, I will talk about the computation of the algebraic duality spectral sequence associated to Y_H and the topological duality spectral sequence converging to the homotopy groups of E_2^{hG_2^1}∧Y_H, a spectrum closely related to L_{K(2)}Y_H.