The generator matrix

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

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+48x^13+192x^14+272x^15+317x^16+408x^17+352x^18+232x^19+128x^20+56x^21+32x^22+8x^23+2x^24

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 0.0281 seconds.