The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 X^2 X X^2 X X 1 1 X 1 X^2 1 X 1
0 X 0 0 0 0 0 0 X^2 X^2+X X^2+X X X^2+X X^2 X X X^2+X X^2+X 0 X^2 0 X X 0 0 0
0 0 X 0 0 0 X X^2+X X^2+X X X 0 X^2+X X^2 X 0 0 X X^2 0 X^2 0 X^2 X^2+X 0 0
0 0 0 X 0 X X X^2+X 0 0 X^2+X X X X X^2+X X 0 X^2 0 0 X^2+X X^2 X^2+X X^2 X^2 0
0 0 0 0 X X 0 X^2+X X X X^2 0 X X^2+X X^2+X 0 0 X X^2+X X^2+X X X X^2 X^2+X X 0
0 0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0
0 0 0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0
0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2
generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.
Homogenous weight enumerator: w(x)=1x^0+26x^17+115x^18+180x^19+288x^20+476x^21+739x^22+1156x^23+1718x^24+2180x^25+2406x^26+2308x^27+1824x^28+1280x^29+742x^30+412x^31+247x^32+130x^33+87x^34+40x^35+16x^36+4x^37+7x^38+2x^40
The gray image is a linear code over GF(2) with n=104, k=14 and d=34.
This code was found by Heurico 1.16 in 4.52 seconds.