The generator matrix

 1  0  0  0  1  1  1  1  0  X  1  1 X^2 X^2+X X^2  1  1
 0  1  0  0  0 X^2  1 X+1  1  1  1 X^2+1 X^2+X  1  1  1  0
 0  0  1  0  1  X  1 X^2  1 X^2+X X^2 X^2+X+1  1 X+1  1  X  1
 0  0  0  1  1 X+1  X X^2+1 X^2+X+1 X+1 X^2+X  1  1 X^2 X^2+1 X^2+X+1  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  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+89x^12+268x^13+596x^14+1006x^15+1330x^16+1554x^17+1408x^18+1020x^19+595x^20+224x^21+76x^22+22x^23+1x^24+2x^25

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.11 in 0.14 seconds.