The generator matrix

 1  0  0  0  1  1  1  0 X^2  1  X  1  1  0  1  1  1  1  0 X^2+X  1  1  1  1  1
 0  1  0  0  0  1  1  1 X^2+X  X  1 X^2+1 X^2+X+1  1 X^2 X+1  1 X+1  1  0 X^2+X  0 X+1  X  1
 0  0  1  0  0  1 X^2+1  X  1  1 X+1 X^2+X X^2 X^2+X+1 X^2+1  X X+1 X^2+X X^2+1 X^2+X X^2 X+1 X^2 X+1 X^2+X
 0  0  0  1  1 X^2 X^2+1  1 X^2+1  X  X X+1  0 X^2+1 X^2+X+1  1 X^2+X+1  0 X+1  1 X^2+1 X^2+X X+1 X^2+1  1
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 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+244x^20+464x^21+684x^22+908x^23+1181x^24+1360x^25+1022x^26+936x^27+723x^28+384x^29+208x^30+44x^31+26x^32+6x^34+1x^36

The gray image is a linear code over GF(2) with n=100, k=13 and d=40.
This code was found by Heurico 1.11 in 0.296 seconds.