The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X 0 X^2+X X^2 X X^2 X X^2 X 0
0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2
generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+20x^22+46x^24+128x^25+40x^26+16x^28+4x^30+1x^48
The gray image is a linear code over GF(2) with n=100, k=8 and d=44.
This code was found by Heurico 1.16 in 0.00659 seconds.