The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1
0 X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X 0 X^2+X X^2 0 X^2 X^2+X X
0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 0 0
generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+24x^14+46x^16+128x^17+32x^18+16x^20+8x^22+1x^32
The gray image is a linear code over GF(2) with n=68, k=8 and d=28.
This code was found by Heurico 1.16 in 0.00247 seconds.