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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+45x^88+440x^90+8x^92+8x^94+7x^96+3x^120

The gray image is a linear code over GF(2) with n=720, k=9 and d=352.
This code was found by Heurico 1.16 in 0.844 seconds.