58th century

The 58th century was visited once by the Doctor, in an alternate timeline, where he visited Helios 3 in 5738. (PROSE: Spiral Scratch)

Earlier, in 5720, following World War VI, archaeologists on Earth discovered the ancient remains of a Khorlthochloi spaceship, though they never learned anything about its creators or why it had crashed. (PROSE: Synthespians™)

According to the Tenth Doctor, retro-gaming was big in the 58th century, which he described as the far future to 21st century native Rose Tyler. (PROSE: The Price of Paradise)

Behind the scenes
The second "Dr. Who" memo states that "Dr. Who" stole his time machine to escape from his home galaxy in the year 5733. This was changed by The Pilot Episode with Susan's claim of being from the 49th century, but neither dates made it to screen.