The generator matrix
1 0 0 0 0 1 1 1 1 X X^2 1 X^2+X X X 1
0 1 0 0 0 0 X^2+1 X+1 1 1 1 X^2+1 1 X^2 X 0
0 0 1 0 0 1 X+1 X 0 1 X X 1 1 1 0
0 0 0 1 0 1 X X+1 0 X^2+1 0 X X X X+1 0
0 0 0 0 1 1 0 X^2 X+1 X^2+1 X 0 X^2+1 X^2+X 1 0
0 0 0 0 0 X X X X^2+X 0 X X^2 X X^2+X X^2+X X^2
generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+52x^9+396x^10+1330x^11+3413x^12+8034x^13+15440x^14+23338x^15+26992x^16+23362x^17+15486x^18+8118x^19+3467x^20+1190x^21+324x^22+110x^23+15x^24+2x^25+2x^26
The gray image is a linear code over GF(2) with n=64, k=17 and d=18.
This code was found by Heurico 1.13 in 15.5 seconds.