The generator matrix

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

generates a code of length 46 over GR(64,4) who´s minimum homogenous weight is 311.

Homogenous weight enumerator: w(x)=1x^0+4480x^311+938x^312+8960x^319+1267x^320+15232x^327+1862x^328+7x^336+21x^368

The gray image is a code over GF(8) with n=368, k=5 and d=311.
This code was found by Heurico 1.16 in 0.159 seconds.