The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+90x^81+760x^82+2466x^83+3926x^84+6768x^85+10840x^86+15548x^87+21202x^88+25196x^89+28547x^90+30354x^91+29619x^92+26546x^93+21426x^94+15384x^95+9745x^96+6010x^97+3781x^98+2174x^99+963x^100+408x^101+208x^102+94x^103+46x^104+16x^105+6x^106+10x^107+2x^108+6x^109+2x^111

The gray image is a linear code over GF(2) with n=728, k=18 and d=324.
This code was found by Heurico 1.16 in 863 seconds.