The generator matrix

 1  0  1  1  1  0  1  1 X^2  1  1  X X^2  1  1  1
 0  1  1  0 X+1  1  0 X^2+X+1  1 X+1 X^2+X  1  X X^2  X  0
 0  0  X  0  0  X  X  0 X^2+X  X X^2+X  0 X^2  X  X  0
 0  0  0  X  0  X  X X^2+X X^2  X  X X^2+X X^2+X  0  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 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+50x^10+114x^11+187x^12+440x^13+1013x^14+1466x^15+1628x^16+1536x^17+945x^18+454x^19+225x^20+72x^21+39x^22+14x^23+7x^24+1x^26

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 0.358 seconds.