You cannot. For stability, the tower needs to be in the shape of a pyramid or tetrahedron and 15 stories would take at least 560 glasses. With 286 glasses you can build an 11-story tower.

Note that despite what still pictures may suggest (and what will work more or less for small family-party sized towers) you cannot fill a champagne tower by just pouring into the top glass. Each glass overflows into three others, but each on the "ridge" gets filled only by one of the glasses above it, meaning that it takes 3 times as long to fill. This means that with 11 stories the corner glasses will not be filled till about a quarter-million glassfuls have been poured! Most of this will end up spilling out of central glasses on the bottom layer and being wasted. If the pourer does not realize this quickly the supply may not hold out!
I'm not sure how little waste you can have if you pour over the whole outer surface with a good strategy; the math is unreasonably complicated. In practice it is best to start taking the heap apart and filling individual glasses once puddles start to form.

Have fun!
RD