In this mission, a healthy heroe must take an objective mission and carry them to the terminal. Should he interact with the objective? It is not specified. What happens if the hero is wounded while he is carrying the codes to the terminal?

See Retrieving Tokens. Retrieve requires an interact action unless specified otherwise in the mission rules.

Whenever a figure is defeated (including a hero becoming wounded), any carried token(s) are dropped into the same space as a figure. A carried token can not be voluntarily dropped.

Because only a healthy hero or Han Solo can retrieve a token in this misson (if played as Twin Shadows campaign - if played as a side mission with another campaign the rebels may have an ally other than Han Solo as well), whenever a token is dropped, a different figure needs to pick it up. In some other missions the same hero can spend another interact action to retrieve the token again.