The ARR relic is just a glamour item at this point. You can buy a i120 weapon with Poetics in Mor Dhona and upgrade it to i130, or go through Coil for an i135 weapon (though it may be hard to recruit a group).
Or skip all that and just keep following the main story into Heavensward as you'll get better weapons while leveling.

Having a completed ARR relic lets you skip the first step of the Heavensward Relic quest but it'd be a lot quicker to just do that first step than to go through all the ARR relic quest steps.