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.