The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  2  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1 2a+2  1  1  1  1  1  1  1 2a^2+2  1
 0  1  0  2  2 2a 2a^2+3 a^2+3a 3a^2+2a+3 2a  a 3a^2+2 2a^2+3a+1 a^2+3a+3 2a^2+2a  a a^2+3a+3 2a^2+3a+1 3a^2+2 2a^2+3 3a^2+2a+3 a^2+3a  1 a^2+3a+1 a+2 3a^2+2a+2 a^2+a 2a^2+3a+3 2a^2+2a+3  1 3a^2+3 a^2+3a+1 a^2+a 2a^2+2a+3 3a^2+3  1 3a^2+2a+2 a+2 2a^2+3a+3 2a^2+2a+1 3a a^2+3a+2 a+1 a^2+2 3a^2+3a+3 a^2+3  1 2a^2+2a+1 2a^2+3a+2 a^2+2a 3a+1 a^2+3a+2 3a^2+3a+3 a^2+2a+3  1  1
 0  0  2 2a^2+2 2a^2+2a+2 2a^2 2a 2a+2 2a^2+2a 2a+2 2a 2a^2+2  2  0 2a^2+2a  0 2a^2+2 2a 2a^2+2a  2 2a 2a^2+2a+2 2a^2 2a+2  2 2a^2 2a^2 2a^2  0 2a 2a+2 2a^2+2a+2 2a^2+2 2a^2+2a 2a^2+2a+2 2a+2 2a 2a^2 2a^2+2 2a+2 2a^2+2a 2a 2a^2+2a+2  2 2a  0  2 2a^2+2a+2 2a+2  0 2a^2+2a  2 2a^2 2a^2+2 2a^2+2 2a^2+2

generates a code of length 56 over GR(64,4) who´s minimum homogenous weight is 382.

Homogenous weight enumerator: w(x)=1x^0+5880x^382+2352x^383+91x^384+7056x^390+1568x^391+357x^392+12152x^398+3248x^399+49x^400+7x^440+7x^448

The gray image is a code over GF(8) with n=448, k=5 and d=382.
This code was found by Heurico 1.16 in 0.888 seconds.