The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0  0  2  2  0  0  2  2
 0  0  2  0  0  2  0  2  2  0  2  2  2  2
 0  0  0  2  0  2  2  2  0  0  2  0  0  2
 0  0  0  0  2  2  2  0  0  2  2  2  2  2

generates a code of length 14 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+15x^12+32x^14+15x^16+1x^28

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 0.000676 seconds.