The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1
 0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 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+77x^8+196x^12+128x^14+699x^16+2048x^17+384x^18+416x^20+119x^24+28x^28

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 0.0495 seconds.