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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+135x^28+592x^30+639x^32+544x^34+104x^36+16x^38+16x^40+1x^60

The gray image is a linear code over GF(2) with n=256, k=11 and d=112.
This code was found by Heurico 1.16 in 0.719 seconds.