The generator matrix

 1  0  1  1  1 X^2  1  1  1  X  1  0  1  1  0  1  1
 0  1  1  0 X+1  1  1  0 X^2  1 X+1  1  X X^2+X+1  1  1 X^2+1
 0  0  X  0  0 X^2  0 X^2+X X^2+X X^2  X X^2+X X^2  0  X  X X^2+X
 0  0  0  X X^2  X X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  X X^2+X X^2  X  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+124x^14+112x^15+209x^16+160x^17+194x^18+112x^19+88x^20+16x^22+6x^24+2x^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 1.16 in 0.0337 seconds.