My Barney box was quite long and tall but not too wide - the cage and base were on their side in it. Excuse the messy child bedroom lol. Our 8 year old fitted in it for a game, but I don't think I'm going to keep it as it's big to store and not really needed once the cage is seen to be fine.
As the cage is on it's side like that, the box must be just over 100cm long, about 55cm tall and about 45cm deep.