The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0 2a 2a  2 2a+2 2a+2  2
 0  0  2  0  0 2a+2  2  0 2a 2a 2a  2 2a
 0  0  0  2  0  2 2a+2 2a+2 2a  0 2a  2  0
 0  0  0  0  2 2a+2 2a  2 2a+2  2  0  2 2a+2

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+84x^28+165x^32+180x^36+3072x^39+240x^40+204x^44+138x^48+12x^52

The gray image is a code over GF(4) with n=52, k=6 and d=28.
This code was found by Heurico 1.16 in 0.0206 seconds.