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

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

Homogenous weight enumerator: w(x)=1x^0+108x^90+10x^92+3x^96+4x^98+2x^100

The gray image is a linear code over GF(2) with n=720, k=7 and d=360.
This code was found by Heurico 1.16 in 1.05 seconds.