The codes are concerned with keeping a distance from openings where the products of combustion can enter the house nearby and overhangs and other traps where the gases could collect. The istructions that come with the fireplace should describe minimum distances from other objects.
As the concern is not with other vents that exit, the distance apart from floor to floor should be sufficient as long as there is no overhang or inside corner to collect the fumes. The building inspector has the last word, so consult him before installation.