Can I giveaway game codes?

depends, what games?

Can you be more specific?

Codes for stuff in a game, no.
Codes for a game, i.e. CD Keys, yes.

If by the "game codes" you mean the steam redeemable keys - sure.
The /give all -like cheats are not allowed.

Read the FAQ.

For game and DLC yes, except for betas and item codes

You can only giveaway CD keys that are Steam redeemable, but however not all of these keys are allowed (But steam gifts of these games are allowed)

Games that it's not allowed to giveaway CD key:

Dead Island
Call of Duty: Modern Warfare 3
Bulletstorm
Homefront Shotgun DLC
AI War
Supreme Commander / Forged Alliance
Portal 2
DiRT 3
Puppy Games Keys
Red Orchestra: Ostfront 41-45 (Region Locked)
Dark Messiah of Might & Magic Multiplayer
Eets (in certain amounts)
World of Goo
Puzzle Agent
Risen 2: Dark Waters - Air Temple DLC