Blow the Gates is a side quest in The Darkspawn Chronicles DLC for Dragon Age: Origins. It is available as part of the main quest Massacre in the Market. Use a genlock sapper to destroy the gates to the Alienage.
As soon as the quest Kill Bann Teagan has completed, a genlock sapper will appear inside the courtyard where Teagan and the guards are (it will have a quest marker above its head). You don't need to Enthrall it--simply head towards the Alienage gates and it will follow you. Once you get close enough, the sapper will set to work on the gates, planting some explosives to blow them open.
The quest Stop the Resupply triggers.