The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X^2+X X^2 X X 0 X^2
0 0 X 0 0 X^2 X^2+X X X X X X^2+X 0 0 X X^2 0
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 0 X X^2 0 0 X^2
generates a code of length 17 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+59x^12+80x^13+78x^14+176x^15+371x^16+514x^17+380x^18+184x^19+79x^20+60x^21+51x^22+8x^23+2x^24+2x^25+2x^26+1x^30
The gray image is a linear code over GF(2) with n=68, k=11 and d=24.
This code was found by Heurico 1.16 in 0.0441 seconds.