The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+40x^85+286x^86+352x^87+380x^88+240x^89+252x^90+140x^91+119x^92+84x^93+74x^94+36x^95+33x^96+4x^97+4x^98+1x^100+2x^124

The gray image is a linear code over GF(2) with n=712, k=11 and d=340.
This code was found by Heurico 1.16 in 1.89 seconds.