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 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 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 X 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^6*X+1 a^5*X+a^2 X a^3 1 X+a^3 X+a X a^5*X+a^4 X+a^5 a^5*X+a^6 a^5*X+a^2 a^4*X+a^4 a*X+a X a^4*X+a^6 a^5*X+a^2 a^4*X a^4*X+a^3 a^5*X+a^4 a^4*X+a^6 a*X+a^3 a^2*X a^4*X+a^2 a^3*X+a^4 a^3*X+a^6 a^5*X a^5*X+a^4 X+a^4 a^4*X+a^2 a^4*X+a^2 a^3*X X+a^4 a^2 a^6*X+1 a^6*X X+a^2 a^4*X+1 X+a a^2*X+a^4 1 a^6*X+a^2 X+a^5 0 a^2*X+a^3 a^5*X+1 a^2*X+a^6 a^4*X+1 a^4*X+1 a^4*X+a^4 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 a^5*X a*X a^5*X a*X a^2*X a^2*X 0 X 0 a^3*X 0 0 a^4*X a^4*X a^5*X a^3*X 0 a^6*X a^6*X a^6*X X a^6*X a^6*X 0 a^2*X X a^6*X a^4*X X a^3*X a^4*X a^3*X a^5*X a^4*X a^3*X a^4*X a*X a^3*X a^3*X X a^3*X 0 a^5*X 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 X a^6*X 0 a*X a^6*X X a^3*X a^4*X a^4*X 0 a*X X a^3*X a^4*X a^5*X a*X a^2*X a^3*X a*X X a^5*X a^4*X a^5*X a^2*X a^6*X 0 a^3*X a^2*X X a^3*X 0 a^4*X a^6*X a*X a^5*X X a*X 0 a^4*X a^2*X a^5*X a^5*X a^4*X a*X a^2*X a^3*X 0 X a^4*X 0 a*X generates a code of length 77 over F8[X]/(X^2) who´s minimum homogenous weight is 512. Homogenous weight enumerator: w(x)=1x^0+1337x^512+56x^513+224x^514+1232x^516+6755x^520+1904x^521+1064x^522+8176x^524+13517x^528+7392x^529+4872x^530+16464x^532+22036x^536+22288x^537+11256x^538+34384x^540+30338x^544+25704x^545+11256x^546+25760x^548+15295x^552+196x^560+245x^568+154x^576+98x^584+91x^592+35x^600+14x^608 The gray image is a linear code over GF(8) with n=616, k=6 and d=512. This code was found by Heurico 1.16 in 19 seconds.