The generator matrix

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

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+212x^29+257x^30+390x^31+402x^32+360x^33+206x^34+148x^35+26x^36+36x^37+1x^38+6x^39+3x^40

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 56.7 seconds.