Type 60 was a type of TARDIS used by the Time Lords. It was more advanced than the Type 40 and had a different security lock compared to the older model timeship. Type 60's had failsafe and security mechanisms, and they contained a switch which would shut down the ship.
The Corsair's TARDIS, which they named the Esperanza, was a Type 60; according to this account, the Type 60 TARDIS model was old, and newer models were available but the Corsair favoured their TARDIS as a 'vintage' model. (PROSE: One Virtue, and a Thousand Crimes)
Qixotl's TARDIS was believed to be a Type 60 TARDIS which he had managed to obtain from Gallifrey, but Qixotl had modified the ship so it wouldn't be detected by the High Council, and by that point, he no longer viewed his TARDIS as a TARDIS. (PROSE: Alien Bodies)