The generator matrix

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

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 -3.24e-008 seconds.