The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2 X^2  1  1 X^3+X^2  1 X^3+X^2  0  1  1  1 X^3+X^2  1 X^2  1  X  1  1 X^3+X^2+X X^3+X^2  1  1  1 X^3+X^2+X X^3+X^2+X X^2+X  1  1  X  1 X^3+X  X  X  1 X^3+X^2 X^3+X  1  1  X  1  1 X^3+X^2  1  1  1  1 X^3 X^2  1 X^3  1  1 X^3+X^2 X^2+X X^3+X  1  1 X^3  X X^2+X  1 X^2+X X^3+X  0  1 X^2 X^2+X X^2+X  X X^2+X X^3+X^2  1 X^2+X X^2  1
 0  1  0  0  X X^2+1 X^3  1  1 X^3+X^2+X+1  1  X X^3+X^2+X X+1  1 X^3+X  1 X^2 X^3+X^2+X+1  1 X^2+1 X^3+X X^3+X X^3  X  1  0 X^2+1  1  1 X^2+X+1 X^3+X^2+1 X^3+X^2 X^2 X^3+X^2+X  1 X^3+X+1 X^2+X  1 X^2+X  1  0  0 X^3+X^2 X^2+X  1 X^2+X+1 X^3+X^2+1  1 X^3+X^2+1  0 X^3  X X^3+X+1 X^2+1 X^2  1 X^3+X^2+X X^3  1 X^3+X^2+X X+1  1  1 X^3+X X^3+X^2+X+1 X^2+X  1  1  0 X^3+X^2+1  1 X^3+X X^2+X X^3+X+1  1  1  1 X^2+X  1 X^3+X  1  1  1 X^3+X^2
 0  0  1  0  0 X^3 X^3+X^2+1  1 X^3+1 X^2 X+1  1 X^3+1 X^3+X^2+1 X^2+X X^2+X X^2+X+1  1 X^2+1 X^3+X^2+X X^2+X X^3+X^2 X^3+1  1 X^3 X^2 X^2+1 X^3+X+1 X^2+X+1  X X^3+X^2  1  1  1 X^3+X^2  0 X^3+1  X X^3+X+1  X X^3+X^2+1  1  1 X^3+X^2+X  1 X^2+X X^3+X+1 X^3+X X^3+X+1 X^3+1  1  X X^2+X+1 X^2 X^3 X+1  1 X^3+X^2 X+1 X^2 X^2+X+1 X^3+X^2+X+1  X X+1  1  1  0 X^2+X+1 X^3+X  1  0 X^3+X^2+X  1  1 X^2+X  0 X+1  X  1  1  1  X X^3+X^2+1 X^3+X X^3
 0  0  0  1  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X^2+X X^2+X X^2+1 X^3+X X^3+X^2+1  1 X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+1  0 X^3 X^3+X^2+1  1 X+1 X^3+X X^2+X X^3+X^2+X+1 X^3+X^2+X X^3+X^2+1 X^2 X^3+X^2+X X^3+X^2+X+1 X^2+1 X^2 X^2+X+1  1 X^3+X X^3+X X^3+X^2+X X^3+1 X^2+1 X^2+X  1 X^2+X X^3+X^2 X^3+X^2+X X^3+1  1 X^3+X X^3+X^2+X+1 X^3+X  1  1 X^2+X  1 X^3+X X^3+X X+1  1 X^3+X^2+1 X^3+X^2+X X^3  X X^3+X+1  X X^3+X^2+X+1 X^3+X^2+X X^3+X^2+X+1 X^2 X^2+1 X^2+X X^3 X+1 X+1  0 X^2+X  0 X^2+1 X^3+X^2+X+1 X^3+X^2+1 X^2+1 X^3+X^2+1 X^2+X+1 X^3 X^2 X^3+X^2+X
 0  0  0  0 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2  0 X^2 X^3 X^3+X^2  0 X^3 X^3 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3  0 X^3+X^2 X^2 X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^2 X^2 X^3+X^2  0  0  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+380x^76+1724x^77+3511x^78+6442x^79+10602x^80+15450x^81+20253x^82+26916x^83+29584x^84+31854x^85+30034x^86+27346x^87+21089x^88+15704x^89+9661x^90+5942x^91+2985x^92+1362x^93+701x^94+302x^95+178x^96+60x^97+26x^98+10x^99+10x^100+4x^101+4x^102+2x^103+2x^105+2x^106+3x^108

The gray image is a linear code over GF(2) with n=680, k=18 and d=304.
This code was found by Heurico 1.16 in 813 seconds.