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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+21x^72+48x^73+9x^74+352x^75+10x^76+46x^77+22x^78+1x^82+2x^109

The gray image is a linear code over GF(2) with n=600, k=9 and d=288.
This code was found by Heurico 1.16 in 0.422 seconds.