The generator matrix

 1  0  1  1  1 X^2  1  1 X^2  1  1  1 X^2  1  1  1 X^2+X
 0  1  1  0 X^2+X+1  1 X+1  X  1  X X^2+1 X^2+X+1  1  0  0 X^2+1  1
 0  0  X  0 X^2+X X^2  X X^2  X X^2+X X^2  0 X^2+X X^2+X X^2+X X^2 X^2
 0  0  0  X  0 X^2+X  X X^2+X X^2 X^2  0 X^2+X  0 X^2+X  X  0 X^2
 0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+66x^13+164x^14+260x^15+349x^16+382x^17+376x^18+248x^19+96x^20+62x^21+36x^22+4x^23+2x^24+2x^25

The gray image is a linear code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.16 in 5.46 seconds.