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.