The generator matrix

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

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+48x^5+127x^6+386x^7+934x^8+380x^9+113x^10+50x^11+9x^12

The gray image is a code over GF(2) with n=64, k=11 and d=20.
This code was found by Heurico 1.16 in -4.77e-008 seconds.