The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  X
 0  X  0  0  0  X  0  0 X^2+X X^2  X X^2+X  0 X^2  X X^2
 0  0  X  0  0  X  0  X  X  X X^2  X  0  0 X^2+X  X
 0  0  0  X  0  X  X  X X^2 X^2+X X^2 X^2+X  X  X X^2+X  X
 0  0  0  0  X  X  X X^2 X^2+X  X X^2+X  0 X^2+X X^2 X^2  X
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+162x^10+437x^12+192x^13+1235x^14+832x^15+2430x^16+832x^17+1319x^18+192x^19+431x^20+97x^22+29x^24+3x^26

The gray image is a linear code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 0.492 seconds.