The generator matrix

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

generates a code of length 5 over GR(64,4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+70x^16+420x^24+1505x^32+28672x^35+2100x^40

The gray image is a code over GF(8) with n=40, k=5 and d=16.
This code was found by Heurico 1.16 in 0.00868 seconds.