The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^5+172x^6+992x^7+1709x^8+992x^9+156x^10+32x^11+10x^12

The gray image is a code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.016 seconds.