The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+21x^6+25x^8+10x^10+6x^12+1x^14

The gray image is a code over GF(2) with n=16, k=6 and d=6.
This code was found by Heurico 1.16 in 0.000216 seconds.