The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+23x^80+168x^81+223x^82+566x^83+403x^84+772x^85+468x^86+874x^87+499x^88+692x^89+485x^90+732x^91+418x^92+556x^93+235x^94+386x^95+144x^96+200x^97+94x^98+104x^99+43x^100+40x^101+22x^102+20x^103+5x^104+4x^105+5x^106+6x^107+3x^110+1x^114

The gray image is a linear code over GF(2) with n=356, k=13 and d=160.
This code was found by Heurico 1.16 in 5.38 seconds.