The ability to store large amounts of photonic quantum states is regarded as substantial for future optical quantum computation and communication technologies. However, research for multiplexed quantum memories has been focused on systems that show good performance only after an elaborate preparation of the storage media. This makes it generally more difficult to apply outside a laboratory environment. In this work, we demonstrate a multiplexed random-access memory to store up to four optical pulses using electromagnetically induced transparency in warm cesium vapor. Using a Λ-System on the hyperfine transitions of the Cs D1 line, we achieve a mean internal storage efficiency of 36% and a 1/e lifetime of 3.2 µs. In combination with future improvements, this work facilitates the implementation of multiplexed memories in future quantum communication and computation infrastructures.