The generator matrix

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

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+462x^27+2070x^28+4946x^29+7191x^30+11574x^31+12721x^32+12116x^33+7526x^34+4442x^35+1748x^36+598x^37+91x^38+30x^39+10x^40+4x^41+4x^43+2x^44

The gray image is a linear code over GF(2) with n=256, k=16 and d=108.
This code was found by Heurico 1.16 in 18.7 seconds.