The generator matrix

 1  1  1  1  1  1  1  1  X  X  X X^2  X  1  X  1
 0  X  0  X  0  0  X X^2+X X^2  X X^2+X  X  X X^2+X X^2 X^2+X
 0  0  X  X  0 X^2+X  X  0  X  X  0  X X^2+X X^2+X  X  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2
 0  0  0  0  0  0  0 X^2 X^2  0  0 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+72x^10+288x^12+64x^13+688x^14+448x^15+969x^16+448x^17+712x^18+64x^19+264x^20+64x^22+14x^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 3.25 seconds.