We present a family of parity array codes called 3-PLEX for tolerating two disk failures in storage systems. It only uses exclusive-or operations to compute parity symbols. We give two data/parity layouts for 3-PLEX: (a) When the number of disks in array is at most 6, we use a horizontal layout which is similar to EVENODD codes, (b) otherwise we choose hybrid layout like HoVer codes. The major advantage of 3-PLEX is that it has optimal encoding/decoding/updating complexity in theory and the number of disks in a 3-PLEX disk array is less constrained than other array codes, which enables greater parameter flexibility for trade-offs in storage efficiency and performances.