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

generates a code of length 43 over GR(64,4) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+133x^272+616x^280+735x^288+3584x^294+644x^296+25088x^302+553x^304+525x^312+420x^320+266x^328+182x^336+21x^344

The gray image is a code over GF(8) with n=344, k=5 and d=272.
This code was found by Heurico 1.16 in 0.421 seconds.