The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+154x^18+530x^20+96x^21+934x^22+512x^23+1426x^24+832x^25+1474x^26+512x^27+999x^28+96x^29+482x^30+109x^32+28x^34+6x^36+1x^44

The gray image is a linear code over GF(2) with n=100, k=13 and d=36.
This code was found by Heurico 1.16 in 4.99 seconds.