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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+14x^84+30x^85+21x^86+398x^87+17x^88+12x^89+6x^90+6x^93+4x^94+1x^110+2x^119

The gray image is a linear code over GF(2) with n=696, k=9 and d=336.
This code was found by Heurico 1.16 in 0.75 seconds.