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

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+284x^64+48x^65+620x^66+336x^67+593x^68+528x^69+644x^70+304x^71+276x^72+64x^73+228x^74+139x^76+12x^78+15x^80+3x^84+1x^108

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 0.641 seconds.