Final answer:
The Autonomic motor column is associated with the visceral motor function at the level of the medulla, with the medulla oblongata containing the dorsal motor nucleus of the vagus nerve that regulates parasympathetic functions.
Step-by-step explanation:
The column associated with the visceral motor function at the level of the medulla is the Autonomic motor column. This association is because the medulla oblongata, which is part of the brain stem, houses crucial autonomic centers for the control of visceral functions such as heart rate, breathing, blood pressure, and digestion. More specifically, the dorsal motor nucleus of the vagus nerve in the medulla is the motor nucleus for parasympathetic functions, which includes modulating the digestive system through the enteric nervous system, affecting heart rate and relaxing bronchial tubes in the lungs.