The generator matrix

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

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+138x^20+40x^21+204x^22+288x^23+189x^24+368x^25+174x^26+288x^27+179x^28+40x^29+96x^30+34x^32+6x^34+3x^36

The gray image is a linear code over GF(2) with n=100, k=11 and d=40.
This code was found by Heurico 1.16 in 0.118 seconds.