The generator matrix

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

generates a code of length 8 over GR(16,4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+30x^16+60x^20+828x^24+84x^28+21x^32

The gray image is a code over GF(4) with n=32, k=5 and d=16.
This code was found by Heurico 1.16 in -3.62e-008 seconds.