Glaeser's Dominoes

[From Thinking Mathematically, p. 172]

George Glaeser of Strasbourg put a set of dominoes more or less randomly in a flat tray and took a photograph. The exposure was not correct, and although the numbers can be discerned, the positions of the individual dominoes cannot.

Each domino is a rectangle composed of two adjacent squares, each with a number. In the set there is only one domino with each combination of numbers from the numbers 0 through 6. For example, there is one domino with 2,3, and one with 4,4.

Can you reconstruct the dominoes?

3  6  2  0  0  4  4
6  5  5  1  5  2  3
6  1  1  5  0  6  3
2  2  2  0  0  1  0
2  1  1  4  3  5  5
4  3  6  4  4  2  2
4  5  0  5  3  3  4
1  6  3  0  1  6  6