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

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+14x^22+24x^23+17x^24+144x^25+17x^26+24x^27+14x^28+1x^50

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 0.00639 seconds.