The generator matrix

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

generates a code of length 13 over GR(16,4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+48x^37+108x^38+9x^40+48x^41+36x^42+6x^44

The gray image is a code over GF(4) with n=52, k=4 and d=37.
This code was found by Heurico 1.16 in 3.24e-008 seconds.