The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1  1  1  1 X^2  X  1  1  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2  1  X  1 X^3  1 X^3+X^2+X  1  1 X^2  1  1  X  1  1  X  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 X^3 X^2+X  X X^2  1  0  1  1
 0  1 X+1 X^3+X^2+X X^3+X^2+1  1  X X+1  1 X^3+X^2 X^2+1  1 X^2+X+1  1 X^3  1  1 X^2+X X^3+X^2+X+1 X^3+1 X^3+X  1  1  X X^2 X^3+X+1 X^3+X^2+1  1 X^3  1 X^3+X^2+X X^2+X+1  1  1 X^2  1 X^3  1 X+1  1 X^2+1 X^2  1 X^2+X X^3+1  1 X^3+X X^3+X^2+X+1 X^3+X^2 X^2+X  X X^3+X^2+X X^2+X  X X^3+X^2+X X^3  X X^2  0 X^3 X^3 X^2  0  X X^3+X+1 X^2+1 X^3+X+1 X^3+1 X^2+X X^3+X+1 X^3+X^2 X^2 X^2+X+1 X^2+X+1 X^2+1 X^3 X^3+X^2  1  1  1  1 X^3+X^2  1 X^3+X  0
 0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3  0 X^2 X^3+X^2 X^3  0 X^2 X^3+X^2  0 X^2 X^3  0 X^3  0 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^3 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  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+68x^81+284x^82+322x^83+249x^84+358x^85+148x^86+262x^87+211x^88+54x^89+62x^90+20x^91+2x^92+1x^94+2x^95+2x^103+1x^118+1x^124

The gray image is a linear code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.735 seconds.