The generator matrix

 1  0  1  1  1  0  1  1  0  1 X^2  1 X^2+X  1  1 X^2  0
 0  1  1  0  1  1  0 X+1  1 X^2  1 X^2+X+1  1 X^2  X  1  X
 0  0  X  0  0  0  0  0  0 X^2 X^2 X^2+X X^2+X  X X^2 X^2+X  X
 0  0  0  X  0  0 X^2+X X^2 X^2+X  0  X X^2+X X^2+X  X X^2  X  0
 0  0  0  0  X X^2+X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  X X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 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+222x^12+120x^13+676x^14+736x^15+1644x^16+1360x^17+1690x^18+736x^19+697x^20+120x^21+160x^22+27x^24+2x^26+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 26.8 seconds.