The generator matrix

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

generates a code of length 8 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+63x^4+246x^6+399x^8+260x^10+49x^12+6x^14

The gray image is a code over GF(2) with n=16, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00312 seconds.