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  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0  0 X^3  0  0 X^3 X^3 X^3+X^2 X^2  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  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+36x^28+24x^29+27x^30+192x^31+527x^32+144x^33+16x^34+12x^36+24x^37+20x^38+1x^62

The gray image is a linear code over GF(2) with n=256, k=10 and d=112.
This code was found by Heurico 1.16 in 0.031 seconds.