The generator matrix

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

generates a code of length 77 over F8[X]/(X^2) who´s minimum homogenous weight is 519.

Homogenous weight enumerator: w(x)=1x^0+2576x^519+140x^520+784x^521+1120x^522+1680x^523+2408x^524+4984x^525+6832x^526+14280x^527+1141x^528+3360x^529+5824x^530+7280x^531+7840x^532+8288x^533+11200x^534+18872x^535+2415x^536+7056x^537+10080x^538+9072x^539+9352x^540+8792x^541+11312x^542+22008x^543+3808x^544+10304x^545+11648x^546+10640x^547+9072x^548+10192x^549+10080x^550+17528x^551+56x^552+56x^560+42x^568+14x^576+7x^584

The gray image is a linear code over GF(8) with n=616, k=6 and d=519.
This code was found by Heurico 1.16 in 16.5 seconds.