The generator matrix

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

generates a code of length 53 over GR(64,4) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+3444x^360+1176x^362+3136x^363+6972x^368+784x^370+896x^371+11515x^376+1624x^378+3136x^379+56x^384+7x^392+7x^400+14x^408

The gray image is a code over GF(8) with n=424, k=5 and d=360.
This code was found by Heurico 1.16 in 0.168 seconds.