The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  X  0 X+2  2 3X+2 2X+2  X  0 X+2 2X+2 3X  0 3X+2  2  X 3X+2  0  0 X+2 3X  2 2X+2  X  X 2X X+2  2 3X+2 2X 2X+2 3X  X  0 2X 3X+2 3X 2X+2 2X+2 3X+2 3X+2 2X  0 X+2 3X 3X  2  2 2X  X  2 X+2 2X 3X+2 2X+2 3X 2X X+2  2  X 2X X+2 2X+2 3X  0 X+2 X+2 2X  0
 0  0 2X+2  0 2X+2  2  0  2 2X 2X 2X 2X  2 2X+2  2 2X+2  2  0 2X+2  0  0 2X+2  0  2 2X+2 2X 2X+2 2X 2X  2  2 2X 2X 2X 2X+2 2X 2X+2 2X+2 2X 2X+2  0  0  2  2  2  0  2  0 2X 2X 2X 2X+2  2  0  2  2  0 2X  0  0 2X+2  2 2X+2 2X+2  0  0  0  2 2X
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+8x^66+26x^67+182x^68+590x^69+184x^70+22x^71+8x^72+2x^73+1x^136

The gray image is a code over GF(2) with n=552, k=10 and d=264.
This code was found by Heurico 1.16 in 0.422 seconds.