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

generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 352.

Homogenous weight enumerator: w(x)=1x^0+175x^352+1085x^360+2212x^368+2961x^376+448x^378+3542x^384+9408x^386+4011x^392+65856x^394+4592x^400+153664x^402+5061x^408+4088x^416+2835x^424+1610x^432+504x^440+84x^448+7x^456

The gray image is a code over GF(8) with n=456, k=6 and d=352.
This code was found by Heurico 1.16 in 35 seconds.