The generator matrix

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

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+144x^28+192x^29+640x^30+576x^31+1028x^32+576x^33+592x^34+192x^35+128x^36+16x^38+10x^40+1x^48

The gray image is a linear code over GF(2) with n=256, k=12 and d=112.
This code was found by Heurico 1.16 in 0.109 seconds.