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

generates a code of length 69 over GR(64,4) who´s minimum homogenous weight is 456.

Homogenous weight enumerator: w(x)=1x^0+357x^456+819x^464+665x^472+574x^480+28672x^483+490x^488+357x^496+280x^504+175x^512+168x^520+126x^528+49x^536+28x^544+7x^552

The gray image is a code over GF(8) with n=552, k=5 and d=456.
This code was found by Heurico 1.16 in 0.741 seconds.