The generator matrix

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

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+46x^10+80x^11+287x^12+688x^13+726x^14+1792x^15+963x^16+1792x^17+714x^18+688x^19+280x^20+80x^21+50x^22+4x^24+1x^28

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 0.238 seconds.