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

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+141x^80+48x^81+538x^82+188x^83+770x^84+236x^85+764x^86+364x^87+973x^88+388x^89+906x^90+360x^91+819x^92+232x^93+620x^94+172x^95+297x^96+52x^97+128x^98+4x^99+61x^100+4x^101+64x^102+33x^104+16x^106+6x^108+4x^110+2x^112+1x^120

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 6.97 seconds.