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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+84x^87+88x^88+168x^89+92x^90+56x^91+4x^92+8x^93+3x^94+4x^95+3x^96+1x^126

The gray image is a linear code over GF(2) with n=712, k=9 and d=348.
This code was found by Heurico 1.16 in 1.17 seconds.