From the picture and your description it appears the issue has nothing to do with the brick work. You'd have to get out there with a shovel to check but I'm betting that the foundation is insufficiently deep. Are you certain the foundation is a few feet thick? Even if it is it likely requires more depth and possibly lateral support to counter soil erosion. There are ways to brace and reinforce the column without tearing it down, digging down and starting from scratch but I wouldn't recommend it for a DIY project as a mistake could cause the column to topple with a potential for severe injury or death for anyone caught underneath. Best to get a professional who has the expertise and equipment to do the job right.