The generator matrix

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

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+162x^13+341x^14+468x^15+769x^16+636x^17+736x^18+528x^19+292x^20+114x^21+33x^22+12x^23+2x^24+2x^26

The gray image is a linear code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.16 in 0.111 seconds.