The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  X  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X^2+X  0  0
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 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 12.

Homogenous weight enumerator: w(x)=1x^0+50x^12+4x^13+82x^14+100x^15+151x^16+216x^17+158x^18+152x^19+54x^20+36x^21+14x^22+4x^23+2x^26

The gray image is a linear code over GF(2) with n=68, k=10 and d=24.
This code was found by Heurico 1.16 in 0.00874 seconds.