I agree that it will be pretty unstable! I built a stand for my 55 several years ago that was only 12.5" wide, approx 36" tall and just over 7 feet long... it was pretty bad. I ended up using a small 90 degree angle bracket and screwed one side onto one of the support posts nd screwed the other side into the wall!! Make sure you hit a stud! After that, I didn't worry! I can also tell you that when I moved, I re-used the same stand, but in a different location in a different room. This time, I put a sofa right in front of the stand and it could not fall over, plus made a nice place to sit and watch the fish!!
One thing, make sure you account for any HOB filters or the like that might need room behind the tank. I now build my stands wider to accomodate those type of things!
For example: I'm just finishing a new stand for a new 55 gallon I got at the auction. This one is going into the master bedroom at our new house, so the SAF had to be pretty high!! The 55 tank is approx 12.5" wide, the Emperor 400 filter is right about 4.5" out from the tank, so I made the stand 18" wide for a nice round number. Now, I can slide the stand against the wall, but still have the tank out far enough for the filter to slip in behind it. The stand also doubles as a book shelf, so having it stick 4.5" out from the wall was not an option with the wife!!
Anyway, I'd find a way to either make it wider and more sturdy, or anchor it to the wall.
Anyway, best of luck,