The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X
 0  X  2 3X+2  0 3X+2  2 3X  0 2X 3X+2 X+2  2 2X+2 3X+2 3X+2
 0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0
 0  0  0 2X 2X 2X 2X  0 2X  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 14.

Homogenous weight enumerator: w(x)=1x^0+92x^14+325x^16+92x^18+1x^20+1x^28

The gray image is a code over GF(2) with n=128, k=9 and d=56.
This code was found by Heurico 1.16 in 6.87e-008 seconds.