At the risk of being attackedon by many posters, I venture to say that “rebdoniel” is actually right. Inexplicably- certainly if you think mechitza is me’doraisa- the shulchan aruch does not mention mechitza anywhere. I am aware that for over a thousand years, the shuls in europe had balconies and so ,clearly, this separation of sexes during tefillah is very old – but the Shulchan Aruch does not mention it.
May I add that the Rambam says that this balcony in the Bais Hamikdosh was only put up during sukkos but taken down afterwards- so you have the additional problem that, all year round, there was no balcony at all.