The generator matrix
1 0 0 1 1 1 2 1 1 0 1 1 2 1
0 1 0 2 1 3 1 0 1 1 2 3 1 2
0 0 1 1 3 2 1 2 1 2 2 1 2 3
generates a code of length 14 over Z4 who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+9x^12+24x^13+12x^14+5x^16+8x^17+4x^18+1x^20
The gray image is a code over GF(2) with n=28, k=6 and d=12.
This code was found by Heurico 1.16 in 0.00055 seconds.