The generator matrix

 1  0  0  1  1  1  0 X^2  1  1  1 X^2+X  X  1  1  1  1  1  X  1  1  1  1  X  0
 0  1  0  0 X^2+1 X^2+1  1  X X^2  1 X^2+X  1  1 X+1  0 X^2+X+1 X+1  X  X X^2  1 X^2+X+1 X^2  X  1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^2+1  1  0 X^2+X+1 X^2  X  1 X+1 X^2+X  1 X^2+1  1  1 X^2+X+1  1  1
 0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  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+166x^22+112x^23+249x^24+72x^25+217x^26+40x^27+74x^28+24x^29+48x^30+8x^31+12x^32+1x^34

The gray image is a linear code over GF(2) with n=100, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0208 seconds.