The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  1  1
 0  1  0  0 2a+3  2  1  a 3a  1 2a+2  a  0
 0  0  1  0 3a+3 2a+3  1 a+2  2  a 2a+2  3  2
 0  0  0  1  1 3a+3  2  a  0 3a+1 2a+1 a+1 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+141x^28+252x^29+204x^30+924x^31+909x^32+1428x^33+1740x^34+3132x^35+4011x^36+6540x^37+5124x^38+9396x^39+9204x^40+9276x^41+5220x^42+4980x^43+2079x^44+936x^45+30x^48+9x^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 1.92 seconds.