This article is from the Final-Fantasy and other Square Soft Games FAQ, by email@example.com (Nick Zitzmann) with numerous contributions by others.
You need a ROM before you can get a Board. (Sound strange? I realize
that, but that's the way it goes.)
Find the ROM in the deserted town on Floor 16. If you can't find the
deserted town, head to the Library and search for it.
Take the ROM to Ameyoko town (in the northeast.) In the far-upper-right
corner of town is a Board Shop - it's tough to find. Go there and use
your ROM to get a Board.
When you have the Board, head back to the Pub and show it to So-Cho so
you can start looking for the plutonium.