The generator matrix

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

generates a code of length 81 over F8[X]/(X^2) who´s minimum homogenous weight is 547.

Homogenous weight enumerator: w(x)=1x^0+3528x^547+56x^548+112x^549+952x^550+1456x^551+3255x^552+7224x^553+4592x^554+16352x^555+392x^556+1344x^557+5600x^558+6160x^559+10073x^560+13664x^561+6608x^562+23240x^563+1288x^564+2352x^565+7896x^566+8400x^567+11130x^568+13720x^569+7504x^570+24752x^571+1848x^572+3360x^573+10640x^574+9072x^575+11774x^576+15568x^577+6384x^578+21728x^579+49x^584+49x^592+14x^600+7x^608

The gray image is a linear code over GF(8) with n=648, k=6 and d=547.
This code was found by Heurico 1.16 in 31.1 seconds.