The generator matrix

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

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+44x^10+60x^11+173x^12+212x^13+592x^14+428x^15+2249x^16+612x^17+2280x^18+500x^19+610x^20+188x^21+144x^22+36x^23+38x^24+12x^25+12x^26+1x^28

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 0.405 seconds.