The generator matrix

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

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+443x^12+2038x^13+6357x^14+14418x^15+18929x^16+14612x^17+6324x^18+1932x^19+451x^20+22x^21+5x^22+2x^23+2x^26

The gray image is a code over GF(2) with n=128, k=16 and d=48.
This code was found by Heurico 1.16 in 6.12 seconds.