The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+71x^8+160x^10+272x^11+288x^12+928x^13+1014x^14+1520x^15+2567x^16+2752x^17+2552x^18+1520x^19+1008x^20+928x^21+308x^22+272x^23+161x^24+56x^26+6x^30

The gray image is a linear code over GF(2) with n=68, k=14 and d=16.
This code was found by Heurico 1.16 in 0.49 seconds.