A cheap solution is a wall-mounted bike holding stand. The simple ones are just a couple of prongs that stick out from the wall and support the top tube of your bike. Something like this is $US40 or you can get fancy with this (will work better with sloping top tubes)
I suspect you could build one out of a 1.5m length of timber and some screws quite easily, although attaching it to the wall would require a little care.
The rope-based hanging bike storage systems also work well for this if you can put up with the bike swinging round. Those allow better access, but the bike moves. A solid wall mount won't move but you have to take the bike down and flip it round to access the other side, and you can't turn the handlebars much.