The generator matrix

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

generates a code of length 12 over GR(16,4) who´s minimum homogenous weight is 32.

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

The gray image is a code over GF(4) with n=48, k=5 and d=32.
This code was found by Heurico 1.16 in 0.172 seconds.