The generator matrix

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

generates a code of length 86 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+408x^83+267x^84+320x^85+112x^86+300x^87+253x^88+352x^89+16x^91+5x^92+12x^95+2x^128

The gray image is a linear code over GF(2) with n=688, k=11 and d=332.
This code was found by Heurico 1.16 in 0.782 seconds.