The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^6+24x^7+9x^8+4x^10+8x^11+6x^12

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 0.000178 seconds.