The generator matrix
1 0 0 1 1 1 X^2+X 1 1 X^2 1 0 X^2 1 X 0 1
0 1 0 1 0 1 1 X X^2+1 1 X^2+X+1 1 0 X^2 X^2+X 0 0
0 0 1 1 1 0 1 1 X+1 X 0 X^2+X+1 X 1 1 1 0
0 0 0 X 0 0 0 0 X^2+X 0 X^2+X X^2 X^2 X^2+X X X 0
0 0 0 0 X 0 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X 0 X X 0 0
0 0 0 0 0 X X^2+X X^2+X X^2 X X^2+X X X^2+X X^2 0 X^2+X 0
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+72x^10+128x^11+590x^12+1096x^13+2305x^14+3836x^15+5233x^16+6220x^17+5175x^18+3928x^19+2398x^20+1056x^21+527x^22+108x^23+66x^24+12x^25+17x^26
The gray image is a linear code over GF(2) with n=68, k=15 and d=20.
This code was found by Heurico 1.16 in 4.29 seconds.