The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+312x^29+120x^30+612x^31+28x^32+608x^33+96x^34+184x^35+72x^37+8x^38+4x^39+2x^40+1x^48

The gray image is a linear code over GF(2) with n=256, k=11 and d=116.
This code was found by Heurico 1.16 in 95.6 seconds.