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

generates a code of length 69 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+152x^65+124x^66+304x^67+274x^68+444x^69+280x^70+224x^71+42x^72+96x^73+39x^74+48x^75+2x^76+12x^77+4x^78+1x^80+1x^122

The gray image is a code over GF(2) with n=552, k=11 and d=260.
This code was found by Heurico 1.16 in 0.484 seconds.