The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+102x^17+181x^18+244x^19+523x^20+632x^21+1136x^22+1808x^23+2241x^24+2612x^25+2197x^26+1816x^27+1323x^28+664x^29+419x^30+208x^31+130x^32+86x^33+34x^34+20x^35+6x^36+1x^38

The gray image is a linear code over GF(2) with n=100, k=14 and d=34.
This code was found by Heurico 1.16 in 5.76 seconds.