The generator matrix

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

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+216x^35+69x^36+336x^39+180x^40+216x^43+3x^48+3x^52

The gray image is a code over GF(4) with n=52, k=5 and d=35.
This code was found by Heurico 1.16 in 0.078 seconds.