The generator matrix

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

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+384x^31+366x^32+384x^33+1152x^35+975x^36+2304x^37+2688x^39+2106x^40+3456x^41+1920x^43+606x^44+39x^48+3x^52

The gray image is a code over GF(4) with n=52, k=7 and d=31.
This code was found by Heurico 1.16 in 47 seconds.