The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who�s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+157x^12+172x^13+756x^14+732x^15+1669x^16+1240x^17+1608x^18+792x^19+778x^20+124x^21+132x^22+12x^23+18x^24+1x^28

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 0.442 seconds.