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
 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
 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 2a^2+2

generates a code of length 40 over GR(64,4) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+196x^272+3794x^280+70x^288+14x^312+21x^320

The gray image is a code over GF(8) with n=320, k=4 and d=272.
This code was found by Heurico 1.16 in 0.0124 seconds.