The generator matrix

 1  0  1  1  1  2 X^2+X  1
 0  1 X+1 X^2+X+2 X^2+1  1  1  2
 0  0 X^2 X^2+2  2 X^2  0 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+47x^6+258x^7+418x^8+252x^9+41x^10+2x^11+5x^12

The gray image is a code over GF(2) with n=64, k=10 and d=24.
This code was found by Heurico 1.16 in 6.87e-008 seconds.