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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+634x^80+1640x^81+4142x^82+6664x^83+10599x^84+15964x^85+20820x^86+25240x^87+30050x^88+30588x^89+29468x^90+26764x^91+21557x^92+15172x^93+10230x^94+6028x^95+3523x^96+1524x^97+858x^98+380x^99+144x^100+64x^101+34x^102+12x^103+15x^104+8x^105+16x^106+4x^108+1x^112

The gray image is a linear code over GF(2) with n=712, k=18 and d=320.
This code was found by Heurico 1.16 in 859 seconds.