The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+168x^32+192x^33+222x^36+1152x^37+366x^40+1728x^41+228x^44+33x^48+6x^52

The gray image is a code over GF(4) with n=52, k=6 and d=32.
This code was found by Heurico 1.16 in 0.012 seconds.