The generator matrix

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

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+110x^12+136x^13+445x^14+768x^15+1201x^16+752x^17+439x^18+128x^19+94x^20+8x^21+11x^22+2x^24+1x^26

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 0.047 seconds.