The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  X  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 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  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  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+110x^16+66x^18+84x^20+64x^21+44x^22+256x^23+176x^24+2432x^25+190x^26+256x^27+104x^28+64x^29+136x^30+33x^32+62x^34+4x^36+12x^38+2x^42

The gray image is a linear code over GF(2) with n=100, k=12 and d=32.
This code was found by Heurico 1.16 in 0.289 seconds.