The generator matrix

 1  1  1  1  1  1  1  1
 0  2  0  0  0  2  2  2
 0  0  2  0  2  2  2  0
 0  0  0  2  2  0  2  2

generates a code of length 8 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+30x^8+1x^16

The gray image is a code over GF(2) with n=16, k=5 and d=8.
This code was found by Heurico 1.16 in 0.000163 seconds.