The generator matrix

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

generates a code of length 8 over GR(16,4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+18x^20+222x^24+6x^28+9x^32

The gray image is a code over GF(4) with n=32, k=4 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.