The generator matrix
1 1 1 1 2 1
0 2 0 0 2 0
0 0 2 0 2 0
0 0 0 2 2 0
generates a code of length 6 over Z4 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+6x^4+8x^5+4x^6+8x^7+1x^8+4x^10
The gray image is a code over GF(2) with n=12, k=5 and d=4.
This code was found by Heurico 1.16 in 7.3e-005 seconds.