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.