The generator matrix

 1  0  0  1  1  1  1  1 2a+2  1  1  0 2a
 0  1  0  1  a 3a+3  0  1  1 2a+3  0  2  1
 0  0  1 3a+3  a  1  a  1 2a+1  a a+2  1 2a+1
 0  0  0  2  0  2  0  2 2a+2 2a 2a+2  0 2a+2
 0  0  0  0  2 2a+2 2a  2 2a 2a+2  2 2a  0

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

Homogenous weight enumerator: w(x)=1x^0+339x^28+144x^29+288x^30+1548x^32+1728x^33+2592x^34+5640x^36+8928x^37+7776x^38+11022x^40+13248x^41+7776x^42+3843x^44+528x^45+117x^48+18x^52

The gray image is a code over GF(4) with n=52, k=8 and d=28.
This code was found by Heurico 1.16 in 13.1 seconds.