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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+621x^82+2058x^83+3951x^84+5476x^85+8622x^86+10060x^87+13220x^88+14186x^89+15395x^90+13922x^91+13545x^92+9888x^93+8424x^94+5164x^95+3089x^96+1804x^97+1010x^98+286x^99+170x^100+108x^101+40x^102+10x^103+8x^104+10x^105+2x^107+2x^111

The gray image is a linear code over GF(2) with n=720, k=17 and d=328.
This code was found by Heurico 1.16 in 215 seconds.