The rate performance of wireless coded caching schemes is typically limited by the lowest achievable per-user rate in the given multicast group, during each transmission time slot. In this paper, we provide a new coded caching scheme, alleviating this worst-user effect for the prominent case of multimedia applications. In our scheme, instead of maximizing the symmetric rate among all served users, we maximize the total quality of experience (QoE); where QoE at each user is defined as the video quality perceived by that user. We show the new scheme requires solving an NP-hard optimization problem. Thus, we provide two heuristic algorithms to solve it in an approximate manner; and numerically demonstrate the near-optimality of the proposed approximations. Our approach allows flexible allocation of distinct video quality for each user, making wireless coded caching schemes more suitable for real-world implementations.