A long-lived and multimode quantum memory is a key component needed for the development of quantum communication. Here we present temporally multiplexed storage of five photonic polarization qubits encoded onto weak coherent states in a rare-earth-ion doped crystal. Using spin refocusing techniques we can preserve the qubits for more than half a millisecond. The temporal multiplexing allows us to increase the effective rate of the experiment by a factor of five, which emphasizes the importance of multimode storage for quantum communication. The fidelity upon retrieval is higher than the maximum classical fidelity achievable with qubits encoded onto single photons and we show that the memory fidelity is mainly limited by the memory signal-to-noise ratio. These results show the viability and versatility of long-lived, multimode quantum memories based on rare-earth-ion doped crystals.