The generator matrix

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

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+92x^12+64x^13+504x^14+704x^15+1385x^16+704x^17+480x^18+64x^19+84x^20+8x^22+6x^24

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 0.063 seconds.