The generator matrix

 1  0  1  1  1 X^2+X  1  1  2  1  1 X+2  1  1 X^2  0
 0  1 X+1 X^2+X X^2+3  1 X^2+X+1  2  1 X+2 X^2+1  1 X+1 X^2+X+3  2  1
 0  0 X^2  0 X^2+2  2 X^2 X^2+2 X^2  2  0  2  0  0 X^2  0
 0  0  0  2  0  2  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  2  0  2  0  0  2  2  2  0  2  0  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+22x^12+192x^13+384x^14+960x^15+983x^16+976x^17+376x^18+160x^19+18x^20+16x^21+8x^22

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 0.046 seconds.