The generator matrix

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

generates a code of length 8 over Z4 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+68x^4+144x^5+224x^6+352x^7+438x^8+352x^9+224x^10+144x^11+68x^12+16x^13+1x^16

The gray image is a code over GF(2) with n=16, k=11 and d=3.
This code was found by Heurico 1.16 in 0.0068 seconds.