The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^64+248x^65+482x^66+504x^67+406x^68+560x^69+328x^70+496x^71+420x^72+216x^73+178x^74+24x^75+38x^76+4x^78+2x^80+1x^128

The gray image is a code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 118 seconds.