The generator matrix

 1  0  1  1  1  0  1  1  0  1  0  2  2  1
 0  1  1  0  1  1  0  3  1  0  1  2  2  3
 0  0  2  0  0  2  2  0  0  2  2  2  2  2
 0  0  0  2  0  2  2  2  0  2  0  0  2  0
 0  0  0  0  2  2  2  0  2  0  2  0  2  0

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

Homogenous weight enumerator: w(x)=1x^0+70x^12+47x^16+10x^20

The gray image is a code over GF(2) with n=28, k=7 and d=12.
This code was found by Heurico 1.16 in 0.00875 seconds.