The generator matrix

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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+218x^81+626x^82+748x^83+582x^84+464x^85+350x^86+308x^87+274x^88+158x^89+100x^90+72x^91+93x^92+60x^93+18x^94+16x^95+1x^96+4x^97+1x^100+2x^102

The gray image is a linear code over GF(2) with n=680, k=12 and d=324.
This code was found by Heurico 1.16 in 12.2 seconds.