The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+11x^86+100x^87+222x^88+332x^89+283x^90+44x^91+24x^92+4x^93+1x^110+1x^112+1x^130

The gray image is a linear code over GF(2) with n=712, k=10 and d=344.
This code was found by Heurico 1.16 in 0.516 seconds.