The generator matrix

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

generates a code of length 83 over F8[X]/(X^2) who´s minimum homogenous weight is 552.

Homogenous weight enumerator: w(x)=1x^0+322x^552+168x^553+112x^556+280x^557+392x^558+1400x^559+770x^560+2968x^561+3248x^564+4760x^565+2520x^566+6944x^567+658x^568+8904x^569+8400x^572+9128x^573+5768x^574+11088x^575+644x^576+12936x^577+23184x^580+23688x^581+11592x^582+23072x^583+399x^584+20720x^585+22400x^588+19488x^589+8400x^590+14840x^591+357x^592+11648x^593+231x^600+259x^608+119x^616+105x^624+147x^632+56x^640+28x^648

The gray image is a linear code over GF(8) with n=664, k=6 and d=552.
This code was found by Heurico 1.16 in 20.7 seconds.