The generator matrix

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

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+306x^80+524x^81+898x^82+1044x^83+1671x^84+1616x^85+2120x^86+2148x^87+2651x^88+2320x^89+2654x^90+2464x^91+2314x^92+2128x^93+1956x^94+1652x^95+1434x^96+904x^97+826x^98+404x^99+358x^100+120x^101+134x^102+32x^103+54x^104+4x^105+18x^106+9x^108+2x^110+2x^112

The gray image is a linear code over GF(2) with n=360, k=15 and d=160.
This code was found by Heurico 1.16 in 65.7 seconds.