The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+45x^10+84x^11+140x^12+248x^13+308x^14+1276x^15+525x^16+2960x^17+534x^18+1228x^19+316x^20+248x^21+132x^22+100x^23+42x^24+5x^26

The gray image is a linear code over GF(2) with n=68, k=13 and d=20.
This code was found by Heurico 1.16 in 0.522 seconds.