Barracks of the thousand does not trigger when Cryptic Coat is cast.
Cryptic Coat is an artifact
Barracks of the Thousand states "When ever you cast an artifact or creature spell using mana produced by Barracks of the Thousand, create a white Gnome Soldier artifact creature token..."
However when using Barracks to the Thousand with Crypic coat, it will not trigger the ability
Barracks of the thousand does not trigger when Cryptic Coat is cast.
Cryptic Coat is an artifact
Barracks of the Thousand states "When ever you cast an artifact or creature spell using mana produced by Barracks of the Thousand, create a white Gnome Soldier artifact creature token..."
However when using Barracks to the Thousand with Crypic coat, it will not trigger the ability