The generator matrix

 1  0  1  1  1  0  1  1  1  1 X^2 X^2  X  0 X^2+X  0
 0  1  1  0  1  1  0 X+1  0 X^2+X+1  X  1  1  1  1  1
 0  0  X  0  0  0  X  0  X  X X^2 X^2  0 X^2  0  X
 0  0  0  X  0  0  X  X X^2 X^2+X  0 X^2  X X^2+X  0  X
 0  0  0  0  X X^2+X X^2  X X^2+X  X X^2+X X^2+X  0  X  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 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+39x^10+104x^11+286x^12+272x^13+1402x^14+616x^15+2663x^16+704x^17+1464x^18+280x^19+242x^20+48x^21+38x^22+24x^23+8x^24+1x^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 0.387 seconds.