The generator matrix

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

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+226x^16+172x^18+992x^20+1968x^22+4956x^24+4264x^26+2672x^28+752x^30+285x^32+12x^34+80x^36+4x^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 3.56 seconds.