The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+546x^81+2058x^82+3676x^83+6017x^84+7780x^85+11327x^86+12128x^87+14740x^88+14890x^89+15018x^90+12398x^91+11044x^92+7476x^93+5630x^94+3088x^95+1771x^96+760x^97+422x^98+182x^99+55x^100+36x^101+5x^102+12x^103+4x^104+2x^106+4x^107+2x^110

The gray image is a linear code over GF(2) with n=712, k=17 and d=324.
This code was found by Heurico 1.16 in 215 seconds.