The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X^2 1 1 X X^2 X X
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X 0 0 X X X^2 0 0 X^2
0 0 X 0 0 X^2 X^2+X X X X X X^2+X 0 X X 0 0 X^2 X X^2 X^2+X X^2+X X X X^2
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X 0 X^2+X X X X^2+X X^2+X X^2+X 0 0 X^2 X X^2+X
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 0 X X^2+X X X^2+X X^2 X^2+X 0 X^2 0 X^2 X X^2+X 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+164x^20+20x^21+272x^22+132x^23+350x^24+216x^25+340x^26+120x^27+242x^28+20x^29+120x^30+4x^31+41x^32+4x^34+2x^36
The gray image is a linear code over GF(2) with n=100, k=11 and d=40.
This code was found by Heurico 1.16 in 0.0991 seconds.