The generator matrix
1 0 1 1 1 X^2+X 1 X^2 1 1 1 X^2 X^2 0 X^2+X 1 X^2 1 1 X^2 1 X^2+X 1 1 X 1
0 1 1 0 X^2+X+1 1 X 1 X+1 X^2+X X^2+1 1 1 1 1 X^2 1 X+1 X+1 1 0 1 0 0 0 0
0 0 X 0 X^2+X 0 0 X^2 X 0 X^2+X X^2 0 X X X X 0 X^2 X X^2+X X^2 X X^2+X 0 0
0 0 0 X 0 0 X^2+X X^2+X X X^2 X X^2+X X^2 X X^2 0 X^2 0 X^2 X X X^2 X 0 X^2 0
0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0
0 0 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0
generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+79x^20+140x^21+166x^22+298x^23+453x^24+606x^25+657x^26+526x^27+439x^28+386x^29+189x^30+70x^31+46x^32+18x^33+11x^34+2x^35+6x^36+2x^37+1x^38
The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.241 seconds.