The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+94x^14+176x^15+169x^16+192x^17+165x^18+112x^19+60x^20+32x^21+20x^22+2x^24+1x^26

The gray image is a linear code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.11 in 3.62e-008 seconds.