The generator matrix

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

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+144x^12+336x^13+478x^14+700x^15+779x^16+680x^17+532x^18+320x^19+100x^20+8x^21+14x^22+4x^23

The gray image is a linear code over GF(2) with n=64, k=12 and d=24.
This code was found by Heurico 1.11 in 0.047 seconds.