The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+28x^16+56x^17+100x^18+158x^19+392x^20+728x^21+1256x^22+1856x^23+2312x^24+2568x^25+2332x^26+1900x^27+1260x^28+712x^29+388x^30+176x^31+91x^32+32x^33+16x^34+6x^35+12x^36+4x^38

The gray image is a linear code over GF(2) with n=100, k=14 and d=32.
This code was found by Heurico 1.16 in 2.71 seconds.