The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1 3X  1  1 2X+2  0
 0  1 X+1 3X+2  3  1 3X+3 2X  1 3X 2X+3  1 X+1 X+3 2X  1
 0  0 2X+2  0  2 2X 2X+2  2 2X+2 2X  0 2X  0  0 2X+2  0
 0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0  0  0  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X  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+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 0.047 seconds.