The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^6+45x^8+28x^10+10x^12

The gray image is a code over GF(2) with n=16, k=7 and d=6.
This code was found by Heurico 1.16 in 0.00034 seconds.