There's not supposed to be a picture here, but we can add one if you'd like!
This gate is located at the south end of 'Limsa Lominsa Upper Decks' (where it says "Zone:" in the upper box). X11-Y14 inside the town! It's right next to the Calamity Salvager, Delivery Moogle. South of 'The Aftcastle' :) It should be in your Aethernet list (interact with the Aetheryte in Limsa lominsa, select 'Aethernet', and it should be the bottom option assuming you've unlocked everything in town.) Teleporting to it that way will take you outside town to Middle La Noscea, but if you turn around and go back inside you'll appear at this gate too :)