The generator matrix

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

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+70x^13+204x^14+194x^15+437x^16+260x^17+448x^18+172x^19+168x^20+54x^21+20x^22+18x^23+2x^24

The gray image is a linear code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.11 in 1.05e-007 seconds.