The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 a^6*X  1  1  1  X  1  1  1  1  1  1  1  1 a^3*X  1  1  1  1  1  1  1  1  1 a^5*X  1  1  1  1  1  1  1  1 a*X  1  1  1  1  1  1  1  1 a^2*X  1  1  1  1  0  1 a^4*X  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1 a^4*X
 0  1  0  1  a a^2 a^6*X+a^3 a^6*X+a^4 a^5 a^6 a^6*X a^6*X+1 a^6*X+a a^6*X+a^5  1 a^6*X+a^2 a*X X+a^5  1 a^2*X+a^2 a^5*X+1 a^3 a^4*X+a a^3*X+a^2 X+a^3 a^4*X+a^6 X+a  1 a^2*X+a^3 a^4*X+a^5  X a^4*X+1 a^6*X+1 a^2 a^5 a^3*X+a a^4*X+a^4  1 a^5*X+a a^6*X+a^2 a^3*X+a^6 a^2*X+a^6 a^3*X+1  0 X+a^3 a*X+a^5  1 X+a^2 a^5*X+a^4 a^5*X+a^5 a^5*X a^2*X+a^6 a*X+a^6 X+a^6 X+a^4  1 X+a^4 a^5*X+1 a^3*X+a^6  a a^2*X a^5*X+a^3  1 X+a^2 a^3*X+a^4 a^5*X+a^6 a*X+a^5 a^5*X+a^4 a^4 a^6*X+a a^6*X+a^3 a^5*X+a^2 a^6*X  1  1 a^5*X+a^6 a*X+a^4 a*X+a^2 a^4*X+a^5  1
 0  0  1 a^6  a a^4  1 a^5 a^3 a^2 a^3*X+1 a*X+a^5 a*X+a^4 X+a^2 X+a^6 a*X+a^3 a*X+a a^6*X+a^5 a^2*X+a a^4*X+a^2 a^6*X+a^3 a^3*X+a a^3*X+a^5 a^6*X a^6*X+a^6 a^2*X+a^3 a^3*X+a^6 X+1 a^2*X+a^2 X+a^6 a^2*X+a^4 a^4*X+a^4 a^6*X+1 a*X+a^5 a^4*X+1 a*X+1 a^2*X+a^6 a^4 a^3*X+a^3 a^2*X+a a^4*X+a a^4*X+a^6 a^5*X+a a*X+a^2 a^5*X+a^5 a^5*X+a^4 a^4*X+a^3 a^2*X+1 a^6*X+a^2 a^2 a^2*X a^4*X+1 a^4*X+a^2 a^4*X+a^6 X+a^3 a^4*X+a^5 X+a^5 X+1 a^2*X a^5*X+a^4  1 a^6*X+a^2 a^2*X+a^2 X+a^3 a^5*X+a^5 a^4*X+a X+a X+a^4 a^5*X+a a^6*X+a^5 a^4*X+a^4 a^2*X+a a^3*X+a^4 a^3*X a^5*X+a^2 a^3*X+a^3 a^3*X+1  X a^3*X+1  1

generates a code of length 80 over F8[X]/(X^2) who´s minimum homogenous weight is 540.

Homogenous weight enumerator: w(x)=1x^0+3304x^540+56x^542+1400x^543+2562x^544+1736x^545+5208x^546+7616x^547+14952x^548+1456x^550+8176x^551+8708x^552+4816x^553+10640x^554+11816x^555+19712x^556+2296x^558+13944x^559+11445x^560+5320x^561+12376x^562+12656x^563+20776x^564+3360x^566+15904x^567+13475x^568+6048x^569+11200x^570+10920x^571+20104x^572+70x^576+77x^584+14x^592

The gray image is a linear code over GF(8) with n=640, k=6 and d=540.
This code was found by Heurico 1.16 in 19.1 seconds.