The generator matrix

 1  0  1  1  1 X^2  1  1  1  1  1  1  1  0  1  1
 0  1  1  0 X+1  1  0 X+1 X^2  X X+1  X  0  X  X  0
 0  0  X  0  X X^2  X X^2  X X^2+X  0  0 X^2+X  X  X  0
 0  0  0  X  X X^2+X X^2+X X^2 X^2  0 X^2 X^2+X  X X^2+X  X  0

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+50x^12+68x^13+115x^14+204x^15+189x^16+164x^17+103x^18+68x^19+46x^20+8x^21+5x^22+2x^24+1x^26

The gray image is a linear code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 0.00908 seconds.