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

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+34x^90+12x^91+1x^92+6x^93+1x^94+4x^95+2x^96+2x^97+1x^98

The gray image is a linear code over GF(2) with n=720, k=6 and d=360.
This code was found by Heurico 1.16 in 0.516 seconds.