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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+56x^82+256x^83+132x^84+234x^85+80x^86+156x^87+27x^88+44x^89+23x^90+12x^91+2x^93+1x^130

The gray image is a linear code over GF(2) with n=680, k=10 and d=328.
This code was found by Heurico 1.16 in 0.437 seconds.