Pick up this quest in Azys Lla
Go to Mor dhonna speak with Roweena (22,5)
Head upstairs, speak with Syndony (22,5)

At this point if you have a Full Zeta weapon you may trade it in to Syndony to skip this next step otherwise

You will need to Farm fates for certain type of Crystals
Note: You do not have to be on your Main job, you may also level anything 50+ while farming these Crystals

You will need 3 of each Crystal

Sea of Clouds: Luminous Wind Crystals
Azys Lla: Luminous Fire Crystals
Churning Mists: Luminous Lightning Crystals
Coerthas Western Highlands: Luminous Ice Crystals
Dravanian Forelands: Luminous Earth Crystals
Dravanian Hinterlands: Luminous Water Crystals

Once you have all the Crystals, trade them to Syndony to retrieve Astral nodule and umbral nodule

After you obtain these items Head to Azys Lla to complete this Quest. Congratulations you now own as I170 Weapon and your first step towards the Anima Weapon.