The generator matrix

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

generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+154x^11+797x^12+2172x^13+4148x^14+7694x^15+10959x^16+13548x^17+10882x^18+8134x^19+4190x^20+1908x^21+712x^22+178x^23+52x^24+4x^25+2x^26+1x^28

The gray image is a linear code over GF(2) with n=68, k=16 and d=22.
This code was found by Heurico 1.13 in 6.13 seconds.