The generator matrix

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

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+148x^10+490x^12+128x^13+1258x^14+896x^15+2331x^16+896x^17+1298x^18+128x^19+486x^20+110x^22+20x^24+2x^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 1.8 seconds.