The generator matrix

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

generates a code of length 4 over GR(64,4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+42x^16+168x^24+3584x^28+301x^32

The gray image is a code over GF(8) with n=32, k=4 and d=16.
This code was found by Heurico 1.16 in 0.000188 seconds.