The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X X^2 X^2 X^2 X^2
 0 X^2+2  2 X^2  0 X^2+2  2 X^2 X^2+2 X^2  0  2 X^2+2 X^2  2  0

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+59x^16+4x^20

The gray image is a code over GF(2) with n=128, k=6 and d=64.
This code was found by Heurico 1.16 in 3.62e-008 seconds.