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  1  X  1  X  1  1 X^2  1
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2  0 X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^3 X^2 X^3  0  0  0
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3 X^3+X^2  0 X^2 X^2 X^3+X^2 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+33x^28+64x^29+20x^30+248x^31+279x^32+298x^33+29x^34+8x^35+5x^36+20x^37+14x^38+2x^40+2x^41+1x^58

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 0.032 seconds.