The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1
 0  1  1  a 3a+3  0 2a+3  a a+1  1 2a+3 a+1  0
 0  0 2a+2  0  0  2  0 2a 2a 2a+2 2a+2 2a  2
 0  0  0  2  0 2a+2 2a 2a+2  0 2a+2 2a+2 2a+2  2
 0  0  0  0 2a+2  2  2 2a+2 2a 2a  2  0 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+144x^30+165x^32+384x^33+1296x^34+180x^36+2304x^37+3888x^38+240x^40+3456x^41+3888x^42+204x^44+138x^48+12x^52

The gray image is a code over GF(4) with n=52, k=7 and d=28.
This code was found by Heurico 1.16 in 0.149 seconds.