The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  X  X  1  X  X
 0  X  0  0  0  X X^2+X  X X^2  0  0 X^2+X  X X^2 X^2+X X^2
 0  0  X  0  X  X X^2+X  0  0  X  0  X  0  X X^2  0
 0  0  0  X  X  0 X^2+X  X  X  X X^2  X  X  0  0  X
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  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+28x^9+84x^10+124x^11+300x^12+608x^13+796x^14+1300x^15+1717x^16+1264x^17+844x^18+612x^19+268x^20+144x^21+68x^22+12x^23+18x^24+4x^25

The gray image is a linear code over GF(2) with n=64, k=13 and d=18.
This code was found by Heurico 1.16 in 0.325 seconds.