The generator matrix

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

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+137x^12+156x^13+732x^14+740x^15+1713x^16+1256x^17+1640x^18+792x^19+766x^20+124x^21+124x^22+4x^23+6x^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 0.445 seconds.