The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+112x^81+207x^82+304x^83+383x^84+504x^85+551x^86+586x^87+609x^88+584x^89+706x^90+646x^91+595x^92+532x^93+538x^94+424x^95+243x^96+206x^97+145x^98+92x^99+55x^100+54x^101+19x^102+22x^103+19x^104+18x^105+10x^106+6x^107+11x^108+6x^109+2x^112+2x^120

The gray image is a linear code over GF(2) with n=360, k=13 and d=162.
This code was found by Heurico 1.16 in 52.4 seconds.