The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^14+1x^16+2x^20

The gray image is a code over GF(2) with n=28, k=4 and d=14.
This code was found by Heurico 1.16 in 0.000332 seconds.