The generator matrix

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

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+170x^81+453x^82+616x^83+925x^84+998x^85+985x^86+1276x^87+1200x^88+1308x^89+1257x^90+1058x^91+1176x^92+1014x^93+937x^94+840x^95+643x^96+502x^97+385x^98+262x^99+132x^100+98x^101+72x^102+24x^103+18x^104+20x^105+7x^106+4x^107+1x^108+2x^109

The gray image is a linear code over GF(2) with n=360, k=14 and d=162.
This code was found by Heurico 1.13 in 5.81 seconds.