The generator matrix

 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  X  1  X  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  X  X  X  X  X  X  X  X X^2  X  X  X  X  0  1  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3  0 X^3  0 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3 X^3  0 X^2  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+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 X^3 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^2  0 X^3 X^2 X^2  0  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2 X^3  0 X^2  0 X^2 X^3
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3  0  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  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+50x^81+33x^82+126x^83+295x^84+62x^85+274x^86+88x^87+19x^88+46x^89+11x^90+8x^91+5x^92+2x^93+1x^94+2x^99+1x^134

The gray image is a linear code over GF(2) with n=680, k=10 and d=324.
This code was found by Heurico 1.16 in 0.703 seconds.