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  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  1  X  X  X  X X^2  X  X  X  X  X  X  X X^2 X^3 X^2 X^2 X^2
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3  0 X^3 X^2 X^3  0 X^3 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^2 X^3 X^3+X^2 X^3 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^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^2 X^2  0 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^3 X^2 X^3 X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0  0  0 X^2 X^2 X^3+X^2 X^3  0 X^3  0  0 X^2 X^3+X^2 X^2 X^2 X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3  0 X^2
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 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  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^2  0 X^3  0  0  0 X^2 X^2 X^2 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3  0 X^3+X^2 X^2  0 X^3+X^2  0  0 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2  0 X^2 X^3+X^2  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+60x^81+80x^82+140x^83+192x^84+152x^85+154x^86+88x^87+58x^88+44x^89+20x^90+28x^91+4x^92+2x^94+1x^128

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 0.547 seconds.