The generator matrix

 1  0  0  1  1  1 X^2 X^2  1  X  1  1  1  1  1  X  0
 0  1  0  0 X^2+1 X^2+1  1  1 X^2+X  1 X^2+X+1 X^2+X X^2 X^2+X  X  1 X^2+X
 0  0  1 X+1 X^2+X+1 X^2  1  X  0  X X^2+1  X  1 X^2+X+1 X^2+X  0  1
 0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2

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+95x^14+176x^15+177x^16+176x^17+154x^18+144x^19+52x^20+16x^21+31x^22+2x^24

The gray image is a linear code over GF(2) with n=68, k=10 and d=28.
This code was found by Heurico 1.16 in 0.00925 seconds.