The generator matrix

 1  0  0  1  1  1 X^3  1  1  0  1  1  X X^3+X^2+X  1  1  1 X^2 X^3+X^2+X X^3+X  1 X^2+X  1  1  1 X^3+X  1  1  1  1  1  1
 0  1  0  0 X^3+X^2+1 X^3+X^2+1  1 X^3 X^2+1  1 X^3+X X^2+X+1  1  1 X^2+X X^3+X+1 X^2+1  X X^2 X^2+X  0  1 X^3+X^2+X X^3+1 X^3+X^2  1 X^3+X+1 X^3+1 X^3+X^2+X+1 X^3+X+1 X^3+X^2+X X^3
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1 X^3+X^2+X X^3+1 X^3+1 X^2+1 X^3+X  1 X^2 X^2+X X^3+X^2+X+1 X^3+X  1  1  1 X^2+1 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X+1 X^3+1  0 X^2  1 X^2 X^3+X^2
 0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  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+131x^28+730x^29+1117x^30+1286x^31+1876x^32+1206x^33+984x^34+594x^35+141x^36+64x^37+25x^38+24x^39+11x^40+2x^42

The gray image is a linear code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 0.578 seconds.