The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+105x^64+972x^65+2593x^66+5286x^67+9698x^68+14196x^69+20875x^70+26536x^71+33749x^72+33796x^73+33631x^74+27052x^75+22026x^76+14344x^77+8656x^78+4640x^79+2241x^80+960x^81+478x^82+164x^83+76x^84+36x^85+7x^86+12x^87+6x^88+6x^91+2x^92

The gray image is a linear code over GF(2) with n=584, k=18 and d=256.
This code was found by Heurico 1.16 in 633 seconds.