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

generates a code of length 67 over GR(64,4) who´s minimum homogenous weight is 456.

Homogenous weight enumerator: w(x)=1x^0+21x^456+147x^464+3584x^469+336x^472+7x^536

The gray image is a code over GF(8) with n=536, k=4 and d=456.
This code was found by Heurico 1.16 in 0.0486 seconds.