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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+48x^86+32x^87+368x^88+32x^89+12x^90+12x^92+4x^94+1x^112+2x^120

The gray image is a linear code over GF(2) with n=704, k=9 and d=344.
This code was found by Heurico 1.16 in 0.781 seconds.