The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+462x^12+1980x^13+6412x^14+14368x^15+19023x^16+14520x^17+6408x^18+1856x^19+450x^20+44x^21+12x^22

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 6.25 seconds.