The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 1 1
0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2
0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0
0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0
0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0
0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 0
0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 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+40x^20+134x^24+256x^25+55x^28+25x^32+1x^44
The gray image is a linear code over GF(2) with n=100, k=9 and d=40.
This code was found by Heurico 1.16 in 0.0114 seconds.