The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1  1  1  1 X^2  X  1  1  1  1 X^3  1 X^3+X^2+X  1  1  1  X  1 X^2 X^3+X^2+X  1  1  1  1  X  1  0  1  1 X^3+X^2  1  0  0  X  1  0  1  1 X^3  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2+X  1  1  1  1  1  1  1 X^3+X  1  1  1 X^2  1  1 X^2
 0  1 X+1 X^3+X^2+X X^3+X^2+1  1  X X+1  1 X^3+X^2 X^2+1  1 X^2+X+1  1 X^3  1  1 X^2+X X^3+X^2+X+1 X^3+1 X^3+X  1  1  X X^2 X^3+X+1 X^3+X^2+1  1 X^3  1 X^2+X+1 X^3+X^2+X  1  1 X^2  1  1 X^3 X+1 X^2+1 X^3+X  1 X^2  1 X^3+1 X^2+X  1 X^3+X^2+X+1  X  1 X^3+X^2 X^2+X  1  X X^2+X  1 X^3+X^2+X X^3+X+1  1 X^3 X^3+X^2+X  X X^3 X^2 X^2 X^3+X^2  X X^3+X^2  0  X X^3+X^2+X+1 X^3+X^2+1 X^3+X  1 X^3+X X^3+X^2+1  0  X  0  0 X^3  1 X+1 X^2+X+1  0  1 X^3+X+1 X^3+X^2+X+1  1
 0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^2  0  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^2 X^3  0 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2  0 X^3 X^3 X^3  0 X^3+X^2 X^3  0 X^2 X^3 X^3  0 X^2 X^3+X^2 X^3  0 X^2 X^2
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  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+66x^85+424x^86+148x^87+371x^88+118x^89+393x^90+116x^91+232x^92+38x^93+110x^94+24x^95+2x^96+1x^98+2x^105+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 0.875 seconds.