The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+170x^80+578x^81+946x^82+1176x^83+1625x^84+1690x^85+2076x^86+2208x^87+2412x^88+2446x^89+2652x^90+2292x^91+2444x^92+2144x^93+1970x^94+1616x^95+1428x^96+1006x^97+635x^98+470x^99+377x^100+182x^101+122x^102+52x^103+19x^104+2x^105+13x^106+10x^107+4x^108+2x^110

The gray image is a linear code over GF(2) with n=360, k=15 and d=160.
This code was found by Heurico 1.13 in 19.9 seconds.