The generator matrix

 1  1  1  1  X  1  1 X^2
 0 X^2+2  0 X^2  2 X^2  0 X^2+2
 0  0 X^2+2 X^2 X^2 X^2  2  0
 0  0  0  2  0  0  2  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+52x^6+96x^7+221x^8+96x^9+36x^10+10x^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 3.81e-009 seconds.