The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) 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 0.125 seconds.