The generator matrix

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

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+64x^12+320x^13+529x^14+1094x^15+1195x^16+1770x^17+1215x^18+1148x^19+500x^20+244x^21+79x^22+30x^23+2x^25+1x^26

The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 0.363 seconds.