The generator matrix
1 0 0 1 1 1 2 1 1 1 1 1
0 1 0 2 1 3 1 0 1 2 3 2
0 0 1 1 3 2 1 2 1 0 3 1
generates a code of length 12 over Z4 who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+13x^10+24x^11+8x^12+2x^14+8x^15+7x^16+1x^18
The gray image is a code over GF(2) with n=24, k=6 and d=10.
This code was found by Heurico 1.16 in 0.000364 seconds.