The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  X X^2  X  X  X  1  X  X  X  1  1
 0  X  0  0  0  0  0  0 X^2 X^2+X X^2+X  X X^2+X X^2  X  X X^2+X X^2+X  X  X X^2+X X^2  0  0  0
 0  0  X  0  0  0  X X^2+X X^2+X  X  X  0 X^2+X X^2  X  0  0  X X^2  0 X^2  0  0  X  0
 0  0  0  X  0  X  X X^2+X  0  0 X^2+X  X  X  X X^2+X  X  0 X^2  0 X^2 X^2+X X^2+X  0  0  0
 0  0  0  0  X  X  0 X^2+X  X  X X^2  0  X X^2+X X^2+X  0  0  X  X  X  X  0 X^2+X  X  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 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+58x^16+60x^17+245x^18+286x^19+480x^20+804x^21+1198x^22+1694x^23+2083x^24+2442x^25+2136x^26+1842x^27+1246x^28+722x^29+466x^30+266x^31+209x^32+66x^33+51x^34+8x^35+18x^36+2x^37+1x^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 4.06 seconds.