It's Hip to be Square

Arrange two of each of the digits 0 through 9 to form a 20 digit number. The number may not begin with 0. Then score the number as follows:

For every two consecutive digits that form a perfect square, score two points. For every three consecutive digits that that form a perfect square, score three points. A four digit square scores four points, and so on.

For example, if your number was 58738219024719503664, you would get two points for 49, two points for 36, two points for 64, and six points for 219024 for a total of 12 points. You may not count 036 as a three digit square.

What is the maximum number you can score?