The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^6+256x^7+413x^8+256x^9+46x^10+2x^12+1x^14

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 3.81e-009 seconds.