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

generates a code of length 48 over GR(64,4) who´s minimum homogenous weight is 319.

Homogenous weight enumerator: w(x)=1x^0+3976x^319+2723x^320+168x^322+1456x^323+1680x^324+3192x^325+6328x^326+21672x^327+12180x^328+448x^329+2352x^330+9184x^331+5600x^332+7056x^333+8848x^334+32536x^335+14784x^336+3136x^337+8232x^338+21616x^339+10640x^340+11256x^341+13496x^342+42168x^343+17290x^344+35x^352+63x^360+21x^368+7x^376

The gray image is a code over GF(8) with n=384, k=6 and d=319.
This code was found by Heurico 1.16 in 9.23 seconds.