The generator matrix

 1  1  1  1  1  1  1  1
 0 2X  0  0  0 2X  0  0
 0  0 2X  0  0 2X  0  0
 0  0  0 2X  0 2X  0  0
 0  0  0  0 2X 2X  0  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+10x^4+234x^8+10x^12+1x^16

The gray image is a code over GF(2) with n=64, k=8 and d=16.
This code was found by Heurico 1.16 in -1.01e-007 seconds.