The generator matrix

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

generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 382.

Homogenous weight enumerator: w(x)=1x^0+2688x^382+6832x^383+2863x^384+504x^386+1008x^387+2240x^388+5768x^389+15456x^390+21056x^391+9366x^392+3024x^394+3360x^395+4480x^396+7280x^397+23744x^398+30576x^399+13692x^400+7224x^402+6384x^403+7616x^404+12040x^405+29792x^406+34720x^407+10353x^408+28x^416+21x^424+21x^432+7x^448

The gray image is a code over GF(8) with n=456, k=6 and d=382.
This code was found by Heurico 1.16 in 11 seconds.