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

generates a code of length 78 over GR(64,4) who´s minimum homogenous weight is 526.

Homogenous weight enumerator: w(x)=1x^0+2408x^526+602x^528+1792x^529+2520x^530+2464x^531+3640x^532+5768x^533+15232x^534+3199x^536+7560x^537+10360x^538+9912x^539+6664x^540+8400x^541+20720x^542+5873x^544+10864x^545+11144x^546+9072x^547+7112x^548+10248x^549+21504x^550+8575x^552+15624x^553+15400x^554+10808x^555+7672x^556+7840x^557+18984x^558+77x^560+70x^568+35x^576

The gray image is a code over GF(8) with n=624, k=6 and d=526.
This code was found by Heurico 1.16 in 16.6 seconds.