The generator matrix

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

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+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 0.015 seconds.