The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+714x^16+2688x^18+2016x^20+16128x^22+16392x^24+24192x^26+3360x^28+45x^32

The gray image is a code over GF(4) with n=32, k=8 and d=16.
This code was found by Heurico 1.16 in 0.75 seconds.