The generator matrix

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

generates a code of length 6 over Z4 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+12x^1+66x^2+220x^3+495x^4+792x^5+924x^6+792x^7+495x^8+220x^9+66x^10+12x^11+1x^12

The gray image is a code over GF(2) with n=12, k=12 and d=1.
This code was found by an older version of Heurico in 0 seconds.