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

generates a code of length 82 over F8[X]/(X^2) who´s minimum homogenous weight is 554.

Homogenous weight enumerator: w(x)=1x^0+4088x^554+672x^556+56x^557+2072x^558+2520x^559+5635x^560+5488x^561+19376x^562+4144x^564+952x^565+6664x^566+4816x^567+13111x^568+9352x^569+27216x^570+8512x^572+1064x^573+9128x^574+7000x^575+11452x^576+9184x^577+32368x^578+11760x^580+1512x^581+10808x^582+7168x^583+13202x^584+8232x^585+24472x^586+56x^592+7x^600+49x^608+7x^624

The gray image is a linear code over GF(8) with n=656, k=6 and d=554.
This code was found by Heurico 1.16 in 68.6 seconds.