The generator matrix

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

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+118x^12+376x^13+448x^14+784x^15+651x^16+784x^17+472x^18+336x^19+90x^20+24x^21+8x^22+4x^24

The gray image is a linear code over GF(2) with n=64, k=12 and d=24.
This code was found by Heurico 1.16 in 0.0935 seconds.