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Python, 85 bytes
print({(*sorted((i*3**j+j)%14for i in[1,5,j%5^22,9910>>j%5*4]),)for j in range(210)})
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Outputs {(0, 1, 4, 5), (6, 8, 11, 12), (1, 7, 9, 11), (2, 3, 12, 13), (2, 4, 9, 11), (0, 6, 7, 13), (4, 5, 11, 12), (4, 8, 10, 12), (8, 9, 10, 11), (2, 6, 9, 13), (1, 2, 5, 7), ...