The generator matrix

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

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+74x^11+399x^12+1008x^13+2286x^14+3608x^15+5934x^16+5862x^17+6196x^18+3898x^19+2209x^20+796x^21+350x^22+100x^23+33x^24+14x^25

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 seconds.