The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+576x^31+225x^32+1152x^35+576x^36+1344x^39+216x^40+6x^48

The gray image is a code over GF(4) with n=48, k=6 and d=31.
This code was found by Heurico 1.16 in 9.47 seconds.