The generator matrix

 1  1  1  1  X  1  1  0  1  1  X  X  1  1  1  1  1
 0  X  0 X^2+X  X  0 X^2+X  X  0 X^2+X X^2+X X^2+X  0  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  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  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  0  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  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+63x^8+40x^10+176x^12+64x^13+230x^14+256x^15+1031x^16+384x^17+1016x^18+256x^19+224x^20+64x^21+196x^22+41x^24+48x^26+6x^30

The gray image is a linear code over GF(2) with n=68, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0415 seconds.