The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^4+548x^5+3149x^6+14272x^7+29437x^8+14360x^9+3122x^10+512x^11+72x^12+4x^13+1x^14

The gray image is a code over GF(2) with n=64, k=16 and d=16.
This code was found by Heurico 1.16 in 1.13 seconds.