The generator matrix

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

generates a code of length 13 over GR(64,4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+1848x^77+2520x^78+105x^80+2688x^84+25872x^85+15120x^86+231x^88+68096x^91+18816x^92+90552x^93+36120x^94+42x^96+133x^104

The gray image is a code over GF(8) with n=104, k=6 and d=77.
This code was found by Heurico 1.16 in 1.62 seconds.