The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  2  0  2  0 2X  2 2X+2  0  2  0 2X  2 2X  0  0
 0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  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+11x^12+8x^13+12x^14+28x^15+401x^16+20x^17+14x^18+4x^19+3x^20+4x^21+5x^22+1x^30

The gray image is a code over GF(2) with n=128, k=9 and d=48.
This code was found by Heurico 1.16 in 3.81e-009 seconds.