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  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2  0  0 X^3 X^3  0 X^3  0 X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^2 X^3+X^2  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^2 X^3  0 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^3 X^2 X^2 X^2 X^2  0 X^3  0 X^3 X^3  0  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^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^3  0  0 X^3 X^3 X^2 X^3+X^2  0  0 X^3 X^2 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0
 0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  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+13x^86+24x^87+55x^88+344x^89+47x^90+6x^91+6x^92+6x^93+3x^94+2x^95+2x^96+1x^114+2x^121

The gray image is a linear code over GF(2) with n=712, k=9 and d=344.
This code was found by Heurico 1.16 in 0.813 seconds.