The generator matrix

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

generates a code of length 13 over GR(64,4) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+1008x^78+112x^80+1344x^84+6048x^86+210x^88+9408x^92+14448x^94+63x^96+126x^104

The gray image is a code over GF(8) with n=104, k=5 and d=78.
This code was found by Heurico 1.16 in 0.0351 seconds.