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.