The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+24x^5+60x^6+104x^7+653x^8+104x^9+44x^10+24x^11+10x^12

The gray image is a code over GF(2) with n=64, k=10 and d=20.
This code was found by Heurico 1.16 in 3.81e-009 seconds.