The generator matrix

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

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+41x^20+292x^21+399x^22+488x^23+543x^24+634x^25+520x^26+492x^27+327x^28+238x^29+79x^30+28x^31+8x^32+2x^33+2x^34+2x^37

The gray image is a linear code over GF(2) with n=100, k=12 and d=40.
This code was found by Heurico 1.11 in 0.062 seconds.