The generator matrix

 1  0  1  1  1 2X 3X+2  1
 0  1 X+1 X+2 2X+3  1  1 2X
 0  0 2X+2  2 2X 2X+2  0 2X+2

generates a code of length 8 over Z4[X]/(X^2+2X+2) 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 2.1e-008 seconds.