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

generates a code of length 45 over GR(64,4) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+238x^272+1260x^280+2450x^288+3115x^296+3584x^301+4214x^304+50176x^309+4753x^312+175616x^317+5719x^320+5215x^328+3556x^336+1743x^344+462x^352+42x^360

The gray image is a code over GF(8) with n=360, k=6 and d=272.
This code was found by Heurico 1.16 in 26.4 seconds.