The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1 X^2  X  1  1  1
 0  1  0  0  0  1 X^2+X+1  1 X^2+X  1 X^2+X  0  1 X^2+X+1 X^2+1  X
 0  0  1  0  1  1 X^2+X  1  1 X+1  0  1  0 X+1  0 X^2
 0  0  0  1  1  0 X^2+X+1 X+1  X  X X+1  X  1  1 X^2+X+1 X^2+1
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  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+77x^10+308x^11+873x^12+2344x^13+3336x^14+6524x^15+5717x^16+6672x^17+3434x^18+2252x^19+822x^20+328x^21+64x^22+4x^23+10x^24+1x^26+1x^28

The gray image is a linear code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.16 in 3.41 seconds.