The generator matrix

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

generates a code of length 69 over Z2[X]/(X^4) 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 linear code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 117 seconds.