The generator matrix

 1  1  1  1  1  1  X  1  1  X  X  2  X  2  X  X
 0 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X  0

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+25x^16+4x^18+2x^20

The gray image is a code over GF(2) with n=128, k=5 and d=64.
This code was found by Heurico 1.16 in 3.62e-008 seconds.