The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  1  1  1  1  X X^2  1  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  X  X  0 X^2+X X^2+X  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0 X^2  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  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  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+146x^16+18x^19+112x^20+160x^21+338x^22+168x^23+1000x^24+320x^25+824x^26+252x^27+272x^28+32x^29+300x^30+72x^31+5x^32+56x^34+2x^35+18x^38

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 0.247 seconds.