I actually had enough Gil for a small plot...

[Niwashi]

Actually it is level 50.

Requirements to buy a House

Character with level 50 in 1 of the classes.
Second Lieutenant in 1 of the Grand Companies.

Each character that met the requirements can purchase 1 unowned plot of any size, within any Ward.

Well, when I reached Second Lieutenant at level 48, the game told be that Personal Housing has been unlocked (with the fanfare music and big yellow lettering across the center of the screen that it uses on feature unlocks). And the next time I entered a housing area, it repeated that statement (though smaller and by the chat box this time). I haven't tried actually buying one as I'm still saving up money, but I'm pretty sure I could if I had the gil for it.