The generator matrix
1 1 1 1 1 1 1 1 X X X X X X X X
0 X^2+2 0 X^2+2 2 X^2 2 X^2 X^2+2 X^2+2 0 2 X^2 X^2 0 2
0 0 2 2 2 2 0 0 0 2 2 2 2 0 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+125x^16+2x^24
The gray image is a code over GF(2) with n=128, k=7 and d=64.
This code was found by Heurico 1.16 in -1.01e-007 seconds.