In this paper, we study cyclic codes over R=4+u4,u2 = 0. A necessary and sufficient condition for a cyclic code over R to contain its dual is determined. The odd and even length cases are discussed separately to obtain above condition. It is shown that Gray image of a cyclic code over R containing its dual is a linear code over 4 which also contains its dual. We have then obtained the parameters of corresponding CSS-quantum codes over 4. By augmentation, we construct codes with dual-containing property from codes of smaller size containing their duals. Through this construction, we have obtained some optimal quantum codes over 4. Some examples have been given to illustrate the results. © 2018 World Scientific Publishing Company.