The generator matrix

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

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+164x^20+20x^21+272x^22+132x^23+350x^24+216x^25+340x^26+120x^27+242x^28+20x^29+120x^30+4x^31+41x^32+4x^34+2x^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 0.0991 seconds.