The Codex doesn't contain anything you need to know to get through the game and none of the puzzles require outside knowledge so it's best to just dive right into the game. The Codex doesn't spoil the plot or any of the puzzles, it only outlines some of the character's backstories and gives some additional simple explanations about the game world but if you read that before playing the game you won't have anything in your mind to relate the info to. So it makes little to no sense to read the Codex before you complete the game.
The Codex gives some basic descriptions of sci-fi technologies, characters and fictional slang words but if you play the game, you're presented with all the relevant information anyway and in a more organic way.