The generator matrix

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

generates a code of length 55 over GR(64,4) who´s minimum homogenous weight is 376.

Homogenous weight enumerator: w(x)=1x^0+77x^376+329x^384+3584x^385+84x^392+7x^400+7x^432+7x^440

The gray image is a code over GF(8) with n=440, k=4 and d=376.
This code was found by Heurico 1.16 in 0.0275 seconds.