The generator matrix

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

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+51x^32+78x^36+768x^39+48x^40+48x^44+12x^48+18x^52

The gray image is a code over GF(4) with n=52, k=5 and d=32.
This code was found by Heurico 1.16 in 0 seconds.