The generator matrix

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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+556x^81+1983x^82+4074x^83+7066x^84+10664x^85+15829x^86+19854x^87+26232x^88+28558x^89+31381x^90+29934x^91+26522x^92+20488x^93+16068x^94+9904x^95+6404x^96+3438x^97+1720x^98+804x^99+304x^100+206x^101+83x^102+14x^103+27x^104+8x^105+6x^106+8x^107+2x^108+2x^109+2x^110+2x^112

The gray image is a linear code over GF(2) with n=720, k=18 and d=324.
This code was found by Heurico 1.16 in 857 seconds.