The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+148x^13+365x^14+476x^15+741x^16+660x^17+710x^18+512x^19+332x^20+116x^21+21x^22+4x^23+6x^24+4x^25

The gray image is a linear code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.11 in 0.047 seconds.