The generator matrix

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

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+160x^5+828x^6+3360x^7+7693x^8+3360x^9+812x^10+160x^11+10x^12

The gray image is a code over GF(2) with n=64, k=14 and d=20.
This code was found by Heurico 1.16 in 0.14 seconds.