The generator matrix
1 1 1 1 1 1 1 1 X X X X X^2 X^2 X^2 X^2
0 2 0 2 0 0 2 2 0 2 2 0 0 2 2 0
0 0 2 2 0 2 2 0 2 2 0 0 2 2 0 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 6.87e-008 seconds.