The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+474x^12+2072x^13+6138x^14+14496x^15+19041x^16+14768x^17+6116x^18+1888x^19+482x^20+56x^21+2x^22+2x^24

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 6.36 seconds.