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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+30x^64+92x^65+96x^66+800x^67+98x^68+112x^69+30x^70+568x^71+11x^72+36x^73+57x^74+28x^75+52x^76+12x^77+4x^78+12x^79+4x^81+4x^82+1x^130

The gray image is a code over GF(2) with n=552, k=11 and d=256.
This code was found by Heurico 1.16 in 0.5 seconds.