* Talk to Maat at level 61+ to receive this quest.
* After you flag this quest you can be any job or level to trade the seals.
* He will give you four random clues from the list below. Trade a Kindred's Seal to the people you have been assigned (in any order) and they will each in turn give you a different strange stone. (key item)
* Return to Maat when you have collected all four stones.
Further deails and Source: http://wiki.ffxiclopedia.org/wiki/Riding_on_the_Clouds