The generator matrix

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

generates a code of length 32 over Z2[X]/(X^4) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+50x^25+770x^26+2602x^27+6917x^28+16634x^29+29764x^30+48372x^31+52194x^32+47330x^33+30576x^34+17260x^35+6525x^36+2198x^37+676x^38+180x^39+57x^40+28x^41+6x^42+2x^43+2x^44

The gray image is a linear code over GF(2) with n=256, k=18 and d=100.
This code was found by Heurico 1.16 in 209 seconds.