The generator matrix

 1  0  0  0  1  1  1  2
 0  1  0  0  2  1  3  1
 0  0  1  0  3  1  2  3
 0  0  0  1  1  2  3  3

generates a code of length 8 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+112x^6+30x^8+112x^10+1x^16

The gray image is a code over GF(2) with n=16, k=8 and d=6.
This code was found by Heurico 1.16 in 0.000741 seconds.