The generator matrix

 1  1  1  1  2 X^2+2  1  1
 0  X  0  X  X  X X^2  0
 0  0  X  X X^2 X^2+X 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+8x^5+72x^6+194x^7+493x^8+166x^9+72x^10+14x^11+2x^12+2x^13

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.