The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0  1 3X+2 3X+3 3X 2X+2
 0  0  1  1 X+1  X 3X+2  X
 0  0  0 2X  0  0 2X 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+42x^5+537x^6+1496x^7+4045x^8+1492x^9+534x^10+40x^11+2x^12+2x^13+1x^14

The gray image is a code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 0.031 seconds.