The flight instructor and student pilot were performing a soft field takeoff from a 2,340 foot grass runway. During the takeoff the airplane did not accelerate as expected. The flight instructor stated that the airplane lifted off, but the trees at the end of the runway were approaching quickly. The instructor then made a slight turn, aiming for some shorter trees to the right. The airplane did not climb out of ground effect and struck a barbed wire fence. The airplane then impacted the ground just beyond the fence and came to a stop in the upright position. Examination of the airplane revealed substantial damage to the airplane’s fuselage and wings. A review of the airplane’s Pilot Operating Handbook (POH) indicated from grass field, no wind, flaps up, 2000 feet mean sea level, and 88 degree Fahrenheit, the airplane would have a 1,700 foot ground roll and would need 2,827 feet to clear a 50 foot obstacle. The instructor added that the airplane did not perform as the POH indicated.