The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  X X^2  1  0  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X X^2  X X^2+X X^2  X X^2+X  X  0 X^2  X  X  X  0
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X X^2+X  0  X X^2+X  X X^2 X^2  X X^2+X X^2 X^2  0  X
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X X^2+X  X  0  0 X^2+X X^2 X^2+X X^2  0 X^2  X  X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  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+27x^20+70x^21+87x^22+142x^23+149x^24+124x^25+147x^26+100x^27+63x^28+54x^29+21x^30+14x^31+14x^32+8x^33+1x^34+2x^36

The gray image is a linear code over GF(2) with n=100, k=10 and d=40.
This code was found by Heurico 1.16 in 0.027 seconds.