The generator matrix
1 1 1 1 1 1 1 1 X 1 1 1 1 X X X^2 1
0 X 0 0 0 0 0 X 0 X^2 0 X^2+X X^2+X X^2 X X 0
0 0 X 0 0 0 0 X X^2+X 0 X X 0 X^2 X^2+X X^2 0
0 0 0 X 0 0 0 X X^2+X X^2+X X^2 X^2+X X^2 0 X^2+X X^2 X
0 0 0 0 X 0 X X X^2 X X^2+X X^2 X X^2 X X X
0 0 0 0 0 X X X^2 X X^2+X X X X^2+X X 0 0 0
0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2
generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+88x^10+166x^11+299x^12+452x^13+1116x^14+828x^15+4605x^16+1156x^17+4684x^18+920x^19+1154x^20+428x^21+244x^22+132x^23+82x^24+12x^25+12x^26+2x^27+3x^28
The gray image is a linear code over GF(2) with n=68, k=14 and d=20.
This code was found by Heurico 1.16 in 1.76 seconds.