Tsukuyomi was added in patch 4.3 of the Stormblood expansion.
Tsukuyomi becomes available at level 70 as part of the “The Primary Agreement” quest, which is given by Hien – Kienkan (X:6, Y:6).
The trial has a minimum ilevel of 335 to enter and rewards you with:
Allagan Tomestone of Poetics: 12