The generator matrix

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

generates a code of length 80 over GR(64,4) who´s minimum homogenous weight is 540.

Homogenous weight enumerator: w(x)=1x^0+3584x^540+112x^542+1176x^543+1505x^544+3024x^545+6216x^546+4872x^547+15008x^548+560x^549+1232x^550+7000x^551+6552x^552+9856x^553+13440x^554+8624x^555+21224x^556+1120x^557+2576x^558+10696x^559+8155x^560+11536x^561+12712x^562+7560x^563+21840x^564+1904x^565+3248x^566+13384x^567+9254x^568+11424x^569+14224x^570+7616x^571+20776x^572+49x^576+63x^584+14x^592+7x^600

The gray image is a code over GF(8) with n=640, k=6 and d=540.
This code was found by Heurico 1.16 in 17 seconds.