The generator matrix

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

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+533x^12+932x^13+2438x^14+3340x^15+6152x^16+5704x^17+6404x^18+3576x^19+2443x^20+724x^21+406x^22+60x^23+55x^24

The gray image is a linear code over GF(2) with n=68, k=15 and d=24.
This code was found by Heurico 1.13 in 5.59 seconds.