The generator matrix

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

generates a code of length 6 over GR(64,4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+105x^16+840x^24+4515x^32+12600x^40+229376x^42+14707x^48

The gray image is a code over GF(8) with n=48, k=6 and d=16.
This code was found by Heurico 1.16 in 0.548 seconds.