Bungie hasn't made any formal announcement about the upcoming DLC and how it works. Since you purchase the DGE, you never received ANY codes for any part of your Destiny Game. We'll have to wait for clarification, but I would imagine you won't need any codes, it's just included in your purchase.
On your PS4, if you go to Destiny on your dashboard and go down, you should see "related items" and you will be able to see the expansion pass listed under there. Make sure it is verified to your account.
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I probably should have mentioned I have a ps3, sorry. :) ;p
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Same basic Idea on xbone just its under (my games)