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 X^3  1  1  1  1  1  1  1  X  1 X^3  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2+X X^3 X^2+X X^3+X^2  0 X^3+X X^3+X^2  X  0 X^2+X X^2  X  0 X^3+X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^3  X X^2+X X^2 X^3+X^2 X^3  X X^2  X X^3+X^2+X  0  0 X^3+X X^3+X^2 X^3+X^2+X X^3+X^2 X^3 X^3+X^2+X  X X^3+X^2 X^3+X^2+X  X  0 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3+X X^3  X  X X^3 X^3 X^3+X^2 X^2 X^3+X^2+X X^3+X^2 X^2+X X^3 X^3+X^2 X^3+X X^3  0
 0  0 X^3+X^2  0 X^2 X^2  0 X^2  0 X^2 X^3+X^2 X^3  0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3 X^3 X^2 X^2  0 X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^3 X^3 X^3  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  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+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 linear code over GF(2) with n=552, k=11 and d=256.
This code was found by Heurico 1.16 in 0.5 seconds.