Minimum Value From Specified Column Of Range Matrix

I have a 10x10 array that represents different cities that a travelling saleperson can travel to. Rows are cities designated as i values, columns are the same cities and represented by j values. I need to use a For, Next loop to determine the shortest distance (lowest value) in a given column. The i (row) that contained the lowest value is the first city to be visted and a boolean is entered for that j=i column, showing that the city has been visited. When pulling the minimum values from the column I need to ignore 0 values where the distance is between a city and itself. I'm having trouble coming up with a loop that takes identifies the i row with the lowest value that also ignores previously visited cities and takes the boolean into account. Maybe my Excel spreadhseet will clear up what I'm trying to do, The distances were generated using RANDBETWEEN(1,100).