The numerals within the following grid are all base 10.

22 15 8 12 47 55 13 7 18 12 18 53 22 8 12 13 17 18 15 24 12 15 40 12 8 7 23 12 20 8 11 8 37 18 14 31

Select a cell from the first grid, sum its orthogonal neighbours, and into the corresponding cell of the second grid place that sum, for example, the neighbours of 22 are 15 and 13 and so 28 occupies the corresponding cell to 22 in the second table.

Some of the numbers which occur in the second grid will be base 10 squares. Convert each to a double digit base which is greater than 10 and is unique to itself. The new base and the converted number must only use digits 0-9.

The total of those respective bases forms the lowest valued base 10 square number available. What is that square, and what bases did you use?

28 a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a

That other squares are available please feel free to also offer any and the bases used to arrive at it.

Note:1. If the square 25 (base 10) appears then it cannot be represented as base 13, base 14 or base 15 as the respective conversions yield 1C, 1B and 1A even though the bases use only digits within the defined range.