The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 X^2 X 1 X^2
0 X 0 0 0 X X^2+X X X^2 X^2 0 0 X X^2+X X^2 0 0 X X^2+X X^2 X X^2 X^2 X^2+X 0
0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X^2+X X^2 X X X^2 0 0 X^2 X^2 0 X^2+X X
0 0 0 X X 0 X X^2+X 0 X X X^2 X^2 X 0 X^2+X X^2 0 X^2 X X^2 X X X^2 X^2+X
0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2
0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 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+138x^20+40x^21+204x^22+288x^23+189x^24+368x^25+174x^26+288x^27+179x^28+40x^29+96x^30+34x^32+6x^34+3x^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 0.118 seconds.