The 16 fields of a $4 \times 4$ checkerboard can be arranged in 18 lines as follows: the four rows, the four columns, the five diagonals from northwest to southeast, and the five diagonals from northeast to southwest. These diagonals consist of 2, 3, or 4 edge-adjacent fields of the same color; the corner fields of the chessboard alone do not form a diagonal. Now, we place a token in 10 of the 16 fields. Each of the 18 lines containing an even number of tokens earns a point. What is the highest possible point total that can be achieved by optimally placing the 10 tokens? Explain your answer.

Let's think step by step and output the final answer within \boxed{}.
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