So when you activate codie's ability by casting a sorcery or instant and start revealing cards from the top of your deck, if you reveal a permanent spell with adventure, are you able to cast the adventure or does the card get skipped entirely?
No, you won't be able to cast an adventure this way.
715.4. In every zone except the stack, and while on the stack not as an Adventure, an adventurer card has only its normal characteristics.
So the cards that have been exiled with Codie's activated ability are in the Exile zone, and thus are permanent cards, not instant or sorcery cards.
Codie's "you may cast that card" would actually allow you to cast an adventure if "that card" were an adventure, because rule 601.3e allows you to consider alternative characteristics as part of determining if you can cast a spell:
601.3e Some rules and effects state that an alternative set of characteristics or a subset of characteristics are considered to determine if a card or copy of a card is legal to cast. These alternative characteristics replace the object’s characteristics for this determination.
However, Codie will exile cards "until you exile an instant or sorcery card with lesser mana value", and an adventure card will never qualify as that, so you will keep exiling cards, and can only cast the last card you exiled ("that card"). From the original release notes about Adventure:
For example, while it's in your graveyard, Giant Killer is a white creature card whose converted mana cost is 1. It can't be the target of the triggered ability of Mystic Sanctuary.