The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1 X^2 X^2 X^2  X X^2+X  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2 X^2+X X^2+1  1  1  1  X  1 X+1
 0  0  1  1  1  0  1 X^2 X^2+1  1  X X+1  X  1 X^2+X+1  1
 0  0  0  X X^2+X  X  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2  0 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  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+173x^12+260x^13+488x^14+768x^15+730x^16+776x^17+488x^18+224x^19+151x^20+20x^21+16x^22+1x^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 0.164 seconds.