The generator matrix

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

generates a code of length 55 over GR(64,4) who´s minimum homogenous weight is 360.

Homogenous weight enumerator: w(x)=1x^0+588x^360+560x^366+6440x^367+3990x^368+2800x^374+21000x^375+9212x^376+10640x^382+67704x^383+23548x^384+14672x^390+76888x^391+22974x^392+364x^400+315x^408+245x^416+168x^424+28x^432+7x^440

The gray image is a code over GF(8) with n=440, k=6 and d=360.
This code was found by Heurico 1.16 in 28.6 seconds.