Even the smallest motor can move the largest load. The pay off is TIME. Small motors trying to move heavy objects need extensive gearing to increase the available torque, but this gearing means things move slower at the output end. So the first thing you need to establish is the torque capability of the motor, then calculate the torque requirement of the barrel. The ratio between the two is the MINIMUM gear ratio that you need between motor and barrel. I'd recommend you double the gear ratio to provide allowance for the system losses.
Can you confirm the motor model. Playing around with google I turned up Nanotec with motors of the type 5618 M 2008 and 4008
Looking at the part number it might break down as 4T = 4 coils 56 = body dimension 18 = 1.8degrees/pulse M = metric fitting 3 = amps and 008 is possibly the output shaft diameter in mm But that's all guesswork !!