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

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+80x^86+96x^87+170x^88+96x^89+40x^90+19x^92+8x^94+1x^96+1x^124

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 0.766 seconds.