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

generates a code of length 85 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+6x^84+100x^85+6x^86+1x^88+10x^89+1x^90+2x^97+1x^98

The gray image is a linear code over GF(2) with n=680, k=7 and d=336.
This code was found by Heurico 1.16 in 0.672 seconds.