The generator matrix

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

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+39x^12+194x^13+313x^14+898x^15+1223x^16+900x^17+302x^18+172x^19+31x^20+10x^21+9x^22+2x^23+2x^24

The gray image is a code over GF(2) with n=128, k=12 and d=48.
This code was found by Heurico 1.16 in 0.031 seconds.