The generator matrix

 1  0  0  1  1  1 X^2+X+2  1  1  1  0 X+2  1  1  1  1
 0  1  0  1  X X^2+X+1  1 X+2 X^2+2 X^2+3  1  0 X^2+2 X^2+2 X+2  2
 0  0  1  1 X^2+1  X X+1 X^2+X+1  X X^2+X+1 X^2+1  1  0 X^2+X+3 X+1  0
 0  0  0 X^2+2 X^2  2 X^2 X^2+2 X^2  2  2  2  2 X^2+2  2 X^2+2

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+103x^12+492x^13+1610x^14+3518x^15+4923x^16+3596x^17+1556x^18+448x^19+115x^20+8x^21+10x^22+2x^23+2x^24

The gray image is a code over GF(2) with n=128, k=14 and d=48.
This code was found by Heurico 1.16 in 0.422 seconds.