The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+28x^4+48x^5+224x^6+720x^7+2054x^8+720x^9+224x^10+48x^11+28x^12+1x^16

The gray image is a code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in 0.015 seconds.