We propose an application-layer forward error correction (AL-FEC) code rate allocation scheme to maximize the quality of experience (QoE) of a video multicast. The allocation dynamically assigns multicast clients to the quality layers of a scalable video bitstream, based on their heterogeneous channel qualities and video playback capabilities. Normalized mean opinion score (NMOS) is employed to value the client's quality of experience across various possible adaptations of a multilayer video, coded using mixed spatial-temporal-amplitude scalability. The scheme provides assurance of reception of the video layers using fountain coding and effectively allocates coding rates across the layers to maximize a multicast utility measure. An advantageous feature of the proposed scheme is that the complexity of the optimization is independent of the number of clients. Additionally, a convex formulation is proposed that attains close to the best performance and offers a reliable alternative when further reduction in computational complexity is desired. The optimization is extended to perform suppression of QoE fluctuations for clients with marginal channel qualities. The scheme offers a means to trade-off service utility for the entire multicast group and clients with the worst channels. According to the simulation results, the proposed optimization framework is robust against source rate variations and limited amount of client feedback.