The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+144x^35+60x^36+48x^39+3x^48

The gray image is a code over GF(4) with n=48, k=4 and d=35.
This code was found by Heurico 1.16 in 6.87e-008 seconds.