The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) 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 0.015 seconds.