The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+48x^6+108x^7+221x^8+72x^9+48x^10+12x^11+2x^12

The gray image is a code over GF(2) with n=64, k=9 and d=24.
This code was found by Heurico 1.16 in -1.01e-007 seconds.