The generator matrix

 1  0  0  0  1  1  1 X^2+X X^2  1  X  1  1  1 X^2+X  1  1
 0  1  0  0  0  1  1  1  X X^2+X  1 X^2 X^2+1 X+1  1  X  X
 0  0  1  0  1  1  0 X+1  1 X^2+X  1  0  X X^2+X X^2  0  X
 0  0  0  1  1  0 X+1  1  1 X+1  X  0  1 X^2 X^2+1 X+1  0
 0  0  0  0  X  0 X^2+X  X X^2+X X^2  X  X  0 X^2+X X^2+X X^2+X X^2
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  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+88x^11+395x^12+994x^13+2106x^14+4076x^15+5183x^16+7070x^17+5148x^18+4128x^19+2173x^20+958x^21+330x^22+92x^23+23x^24+2x^25+1x^32

The gray image is a linear code over GF(2) with n=68, k=15 and d=22.
This code was found by Heurico 1.16 in 5.02 seconds.