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.