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

generates a code of length 81 over F8[X]/(X^2) who´s minimum homogenous weight is 536.

Homogenous weight enumerator: w(x)=1x^0+154x^536+112x^540+112x^542+448x^543+1470x^544+1736x^545+2240x^548+3304x^550+4200x^551+6349x^552+5936x^553+4816x^556+8232x^558+9800x^559+11284x^560+12096x^561+5936x^564+23352x^566+23352x^567+23660x^568+22736x^569+10752x^572+22344x^574+19544x^575+17542x^576+14840x^577+4816x^580+280x^584+224x^592+168x^600+98x^608+98x^616+56x^624+28x^632+21x^640+7x^648

The gray image is a linear code over GF(8) with n=648, k=6 and d=536.
This code was found by Heurico 1.16 in 20.5 seconds.