The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  1  1  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X X^2 X^2+1 X^2+X+1 X^2 X^2  0
 0  0  X X^2+X  0 X^2+X  X  X X^2+X  0  X  0  X  X X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 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+38x^10+40x^11+106x^12+244x^13+476x^14+740x^15+811x^16+744x^17+472x^18+240x^19+102x^20+36x^21+36x^22+4x^23+4x^24+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 0.0689 seconds.