When you wake up as Zidane, you'll be in the guest room with Mogki the moogle. Go to the conference room.

During the scenes that follow, you will receive a Garnet. Afterward, you'll control the Hilda Garde 3 airship.

Immdiately dock at Lindblum and choose to go to the bridge when you reboard. There is an Elixir at the top of the ladder and a Tent at its base.

There are several things you can do now that you have an airship. Land in the valley beneath Treno where the river emerges from the mountains to visit the north side of South Gate where you'll find an Elixir and another Elixir, 3206 gil and Mosco the moogle. Go over the mountains and revisit the main South Gate entrance, where you'll now be able to reach the treasure chest atop the wagon to find an Elixir.