The generator matrix

 1  1  1  1  1  1  1  1  X  1 X^2  X  X  1  X  1
 0  X  0  0  0  0  0  0 X^2+X  X  X X^2 X^2 X^2 X^2  X
 0  0  X  0  0  0  X X^2+X  X  X X^2  X X^2  0 X^2  X
 0  0  0  X  0  X  X  X X^2 X^2 X^2 X^2  X  0 X^2+X  0
 0  0  0  0  X  X X^2 X^2+X X^2+X X^2 X^2+X  0 X^2+X  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  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+43x^10+74x^11+141x^12+280x^13+469x^14+598x^15+730x^16+820x^17+487x^18+214x^19+143x^20+48x^21+23x^22+10x^23+9x^24+4x^25+2x^26

The gray image is a linear code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.113 seconds.