The generator matrix

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

generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 389.

Homogenous weight enumerator: w(x)=1x^0+5880x^389+1176x^390+1568x^391+147x^392+7056x^397+784x^398+448x^399+301x^400+12152x^405+1624x^406+1568x^407+49x^408+14x^448

The gray image is a code over GF(8) with n=456, k=5 and d=389.
This code was found by Heurico 1.16 in 23.7 seconds.