Enter the Solar and talk to Minfilia to complete the quest.
The Enterprise stands ready to bear you to the Praetorium-- the fortress within a fortress wherein the Ultima Weapon sleeps. Prepare for the fight of your life, and report to Cid at the Ceruleum Processing Plant.
You have arrived at the Praetorium, the stage upon which the fate of the realm shall soon be decided. Fight your way into the depths of the structure, in search of the Ultima Weapon, and when you find the Allagan relic... send a piece of it to each of the seven hells.
The Praetorium can be accessed via the Duty Finder.
With Gaius van Baelsar slain, and the Ultima Weapon destroyed, it would seem that Eorzea may finally look forward to an era of peace. Yet even as the people of the three city-states gather to celebrate their deliverance, a deafening roar reverberates throughout every corner of the realm... A dread primal has awakened.
What fearsome primal is this that has been roused? Perhaps Minfilia will be able to shed some light on the mystery.
In troubled tones, Minfilia reveals to you that shortly after the roar was heard around the land, an aetheric disturbance was observed, bearing a disquieting similarity to a phenomenon recorded five years ago. It would seem that your struggles are far from over. Steel your resolve anew, and set forth to shine the Crystal's light upon the realm.