OpenRocket is your friend. At 14 ounces, it's only going 31 fps leaving a 4' rod, or 34 fps leaving a 6' rod. Not fast enough. Apogee would only be 150 feet. The Estes black powder E motors are not much better, still only mid-30 fps leaving the rod/rail.
Aerotech's product catalog recommends their E15-4 (370') and E30-4 (440') as the smallest/lowest single-use motors. They also show a E11-3 reload for the 24/40 case, good for 450 feet.