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 X 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 a^4*X 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 X 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 a^5*X+a^2 a^3 a^5*X+a^4 X+a^5 X a^5*X+a^4 a^5*X+a^6 1 a^2*X+a^3 X+a a^6*X+1 X+a a^3*X+a^3 a^4*X+1 1 X+a^5 X a^4*X+a^6 a^5*X+a^4 a^5*X+1 X+a^2 X+a a^2*X+a^5 1 a^3*X+a X a^5*X+a^3 a*X+a^6 a^5*X+a^2 a^4*X+a^4 a^5*X+a^6 a^6*X+a^5 a X 1 a^4*X+a^4 a^3*X+a^2 a^3*X+1 a*X+a^5 1 a^6*X+1 a^2*X+a^2 a^6 a^2*X+a^3 1 a^2 a*X+a^6 a^3*X a*X+1 a^5*X+a^2 a^2*X+a^3 1 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^6*X a^4*X a^4*X a^5*X a^6*X a*X a^4*X a*X a^5*X 0 0 X a^6*X 0 X a^2*X a^5*X a^2*X a^4*X a^4*X 0 X a^4*X a^3*X a^2*X a^3*X X 0 a*X a^2*X a^2*X a^5*X 0 a^5*X a^5*X X a*X a^2*X a^3*X a^5*X a^2*X a^5*X a^5*X a^3*X 0 X 0 a^2*X a^4*X a^3*X a^3*X a^4*X a^3*X a*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 a*X a^3*X a^5*X a^2*X 0 a^2*X X a^3*X a^4*X a^6*X a^4*X a^3*X a^3*X 0 0 0 a^4*X a^3*X X a*X a*X a*X 0 a^2*X X 0 0 X a^2*X a^5*X a^2*X 0 a^4*X a^5*X a^4*X a^4*X a*X a*X a^5*X a^2*X a^6*X X a^3*X a^5*X a^2*X a^5*X 0 a^3*X a^5*X a^3*X a*X a*X a^3*X X generates a code of length 82 over F8[X]/(X^2) who´s minimum homogenous weight is 544. Homogenous weight enumerator: w(x)=1x^0+182x^544+112x^546+1568x^551+3920x^552+1288x^553+1568x^554+7336x^559+13020x^560+3472x^561+3976x^562+16968x^567+25396x^568+6496x^569+7112x^570+34552x^575+44730x^576+10864x^577+10024x^578+25592x^583+30604x^584+6552x^585+5880x^586+238x^592+273x^600+119x^608+105x^616+63x^624+63x^632+56x^640+7x^648+7x^656 The gray image is a linear code over GF(8) with n=656, k=6 and d=544. This code was found by Heurico 1.16 in 20.5 seconds.