http://forum.square-enix.com/ffxiv/threads/71222-A-Relic-Reborn-Walkthrough

Right hueh

Important Update:

How to get your Relic Weapon to it's Upgraded (+1) Form.

- x2 Thavnairian Mist (300 Allagan Tomestones of Mythology Each) from Auriana in Revenant's Toll + Relic Weapon + Hyrstmill Forge near Gerolt = Relic Weapon +1

This is the improved relic weapon and rivals the weapons (so far that I've seen) that drop from Bahamut's Coil raid.