The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  1  1  1  1  X  0  0  0
 0  X  0  X  0  0  X X^2+X  0 X^2  X  0 X^2+X  X  X  X  X X^2  0 X^2+X X^2+X X^2  0  X  X
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  0 X^2 X^2+X  X  X X^2+X  X  0 X^2  X  X  X X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 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+153x^20+16x^21+240x^22+128x^23+420x^24+224x^25+320x^26+128x^27+266x^28+16x^29+80x^30+51x^32+5x^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 15.6 seconds.