The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  X  1  X  X  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  X X^2  0 X^2  0
 0  0  X  0  X  X X^2+X  0  0 X^2  X  0 X^2+X  X X^2+X  0
 0  0  0  X  X  0 X^2+X  X  X  0 X^2 X^2+X  0  X  X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 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+53x^10+60x^11+147x^12+272x^13+393x^14+684x^15+864x^16+704x^17+399x^18+276x^19+129x^20+48x^21+51x^22+4x^23+11x^24

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 0.0975 seconds.