Gigantically is the adverb from gigantic: in a gigantic way, to a huge degree. The city has grown gigantically. The project went gigantically over budget. It carries the same “extremely big” idea, but it tells you how something happens or how much, not what something is. Though actually, English speakers do not reach for this word as often as they reach for gigantic. In everyday talk, hugely, massively, or enormously will sound more natural. Gigantically is correct, a little heavy, and a little rare. Save it for when you really want that giant-sized sound.