The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+276x^27+1185x^28+2004x^29+4422x^30+4720x^31+7258x^32+5284x^33+4460x^34+1756x^35+983x^36+260x^37+110x^38+32x^39+13x^40+4x^41

The gray image is a linear code over GF(2) with n=256, k=15 and d=108.
This code was found by Heurico 1.16 in 5.44 seconds.