The generator matrix

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

generates a code of length 13 over GR(64,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+112x^80+210x^88+3584x^91+63x^96+126x^104

The gray image is a code over GF(8) with n=104, k=4 and d=80.
This code was found by Heurico 1.16 in 0.00203 seconds.