The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  0  1  1
 0  X  0  0  0  0  0  0 X^2+X  X  X X^2  0  X X^2+X  X
 0  0  X  0  0  0  X X^2+X  X  0  0 X^2 X^2+X X^2 X^2+X X^2+X
 0  0  0  X  0  X  X X^2+X  0  X  X X^2+X X^2 X^2+X  0  X
 0  0  0  0  X  X  0 X^2+X  X  0 X^2  0  X X^2+X X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 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+60x^9+172x^10+270x^11+422x^12+894x^13+1826x^14+2846x^15+3335x^16+2902x^17+1850x^18+922x^19+442x^20+234x^21+118x^22+58x^23+24x^24+6x^25+2x^26

The gray image is a linear code over GF(2) with n=64, k=14 and d=18.
This code was found by Heurico 1.16 in 9.04 seconds.