The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+68x^5+620x^6+3992x^7+14182x^8+27744x^9+14320x^10+3944x^11+568x^12+92x^13+4x^14+1x^16

The gray image is a code over GF(2) with n=72, k=16 and d=20.
This code was found by Heurico 1.16 in 1.94 seconds.