The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1 X^2+X  1  1  1 X^2  1  1  1  1 X^2  1
 0  1  0  0  0  1 X^2 X^2+1  1 X+1 X^2+X  1 X^2+1  X  1 X^2+1 X^2  0  1 X+1 X^2+X X+1  1  1 X^2
 0  0  1  0  0  1 X^2+1  X X^2+X+1 X^2+1  1 X^2 X^2+X  1 X+1 X^2 X^2+X  1  X X+1  X X^2+X  0 X^2 X^2+X
 0  0  0  1 X+1 X^2 X^2+X+1 X^2+1 X^2+1  1  1 X^2+1  X  0 X^2+X X^2 X^2+X+1 X^2+1  0  X X+1  0 X^2+X  1  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  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+234x^20+480x^21+760x^22+824x^23+1171x^24+1208x^25+1213x^26+936x^27+752x^28+328x^29+194x^30+64x^31+18x^32+9x^34

The gray image is a linear code over GF(2) with n=100, k=13 and d=40.
This code was found by Heurico 1.16 in 0.726 seconds.