The generator matrix

 1  0  0  0  1  1  1 X^2  1 X^2+X  1 X^2+X  X  1  1  0  1
 0  1  0  0  0  1  1  1 X^2+X  1 X^2  0  1  1  X  1 X+1
 0  0  1  0  1  1  0  1  1 X+1  X  1  0  1  X  X  X
 0  0  0  1  1  0  1 X+1  X  0 X+1 X+1  1 X+1  0  X  X
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  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+94x^11+352x^12+1110x^13+1853x^14+4446x^15+4945x^16+7126x^17+5000x^18+4458x^19+1848x^20+1106x^21+314x^22+90x^23+22x^24+2x^25+1x^30

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 5.87 seconds.