The generator matrix

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

generates a code of length 12 over GR(64,4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+672x^78+42x^80+1344x^84+2016x^86+21x^96

The gray image is a code over GF(8) with n=96, k=4 and d=78.
This code was found by Heurico 1.16 in 0.00859 seconds.