The generator matrix

 1  0  0  1  1  1  X X^2  1  1  1  1  0  1  X  1  1
 0  1  0  1  X X^2+X+1  1  0 X^2+X X+1 X^2 X^2+X+1  1  0  1  0  0
 0  0  1  1  1  0  1  1 X^2+1 X^2+X+1  X X^2+1  X X+1 X^2+X X^2+1  0
 0  0  0  X  0 X^2+X X^2  X X^2+X  X X^2 X^2  X X^2  0 X^2  0
 0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  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+70x^12+138x^13+303x^14+502x^15+651x^16+764x^17+675x^18+516x^19+258x^20+122x^21+77x^22+6x^23+12x^24+1x^26

The gray image is a linear code over GF(2) with n=68, k=12 and d=24.
This code was found by Heurico 1.16 in 0.0998 seconds.