Type 53
Type 53 was a type of TARDIS used by Time Lords and more advanced than the Type 40s. The First Doctor nearly borrowed/stole a Type 53 while leaving Gallifrey with his granddaughter, but was convinced by an echo of Clara Oswald to pick the Type 40 because the "navigation system [was] knackered" and "[he would] have much more fun" with it. During the conversation, Susan had already entered the capsule before the Doctor called her back out before entering the Type 40 TARDIS and leaving in that instead. (TV: The Name of the Doctor, COMIC: Hungry Thirsty Roots)
According to another account, the First Doctor nearly stole the Type 53 while alone, but dismissed it as "new-fangled [and] soulless" and went in favour of the Type 40. The Doctor found the Type 53 TARDIS on a construction palette with its specifications listed while the Type 40 was not far away. According to this account, the Type 53 model was one of the latest TARDISes produced by the Time Lords. (PROSE: Lungbarrow)
Despite being newer than the Doctor's TARDIS, the Eleventh Doctor described it as "crummy [and] old". (COMIC: Hungry Thirsty Roots)
