The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1
 0  X  0  0  0  X X^2+X  X  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  X  0  X  X X^2+X  0  0  X  X  X  0 X^2+X  0  0  0
 0  0  0  X  X  0 X^2+X  X  X  X  0 X^2+X  X  0  X  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  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+58x^8+16x^9+119x^10+272x^11+493x^12+480x^13+1289x^14+1520x^15+2141x^16+3616x^17+2118x^18+1520x^19+1298x^20+480x^21+514x^22+272x^23+104x^24+16x^25+51x^26+1x^28+5x^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 0.715 seconds.