The generator matrix

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

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+20x^6+68x^7+89x^8+56x^9+12x^10+4x^11+6x^12

The gray image is a code over GF(2) with n=64, k=8 and d=24.
This code was found by Heurico 1.16 in 3.62e-008 seconds.