The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  0  X  1  1  1 X^2  0  X  1  X  1  1
 0  X  0  0  0  X X^2+X  X  0  0 X^2  X X^2+X  X X^2 X^2  0  0  X  0  X X^2 X^2+X X^2  0
 0  0  X  0  X  X X^2+X  0  0 X^2 X^2+X  0 X^2+X  X  X X^2+X X^2  X  0  X X^2  0 X^2+X  0  0
 0  0  0  X  X  0 X^2+X  X  X X^2  X X^2+X X^2+X  X X^2 X^2  X X^2+X  X  0 X^2+X X^2  X  X  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  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+57x^16+122x^17+184x^18+212x^19+455x^20+816x^21+1172x^22+1744x^23+2200x^24+2404x^25+2208x^26+1800x^27+1246x^28+704x^29+488x^30+304x^31+124x^32+50x^33+40x^34+36x^35+11x^36+4x^38+2x^40

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 3.88 seconds.