The generator matrix

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

generates a code of length 44 over GR(64,4) who´s minimum homogenous weight is 296.

Homogenous weight enumerator: w(x)=1x^0+1400x^296+1680x^297+840x^298+1176x^299+4760x^304+3360x^305+1008x^306+784x^307+8603x^312+5712x^313+1736x^314+1624x^315+49x^320+14x^328+7x^344+14x^352

The gray image is a code over GF(8) with n=352, k=5 and d=296.
This code was found by Heurico 1.16 in 0.155 seconds.