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.