The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  0  1  X  1  X  1  1  1  1  1  1  1  X  1 X^2  1  1  1  1 X^2  X  1  1  1  0  1  1 X^2+X  1  X  1  1 X^2  1 X^2+X  1  1  1  1 X^2+X  1  1  1  0  1  1  1 X^2  1  1  1  0  1  1  1 X^2  1  0 X^2  X  1  1  1 X^2+X  1  1  1 X^2+X  1  1  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1  0 X^2+1  1  1 X+1  1 X^2+X  1 X+1 X^2+1 X^2 X^2+X  0  1 X^2+X+1  1 X^2  1  X X^2+1 X^2+X X+1  1  1 X^2+1 X^2+X X^2+X+1  1 X^2+X X^2+X+1  1  0  1  0 X^2+X  1 X^2+X  1 X+1 X+1  0 X^2+X+1  1  X  X X^2  1  X  1  1  1 X+1 X+1 X^2  1 X^2+1 X^2+X X^2  1 X^2+X  1  0 X^2+X  1 X+1 X^2+1  1  0 X^2 X+1  1 X^2 X^2+1 X^2+1 X^2  1 X+1
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X  X X^2 X^2+X  0 X^2  0 X^2+X X^2 X^2 X^2  X X^2+X X^2+X  X  X  0 X^2+X X^2+X  X  X X^2+X X^2+X  0  0 X^2 X^2+X X^2+X  0 X^2  0  0 X^2  0  0 X^2 X^2+X  0  0 X^2  X X^2+X  X X^2 X^2+X X^2+X X^2  X  X X^2+X  0 X^2+X X^2+X  0 X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  0  0 X^2+X X^2+X  X X^2+X  X X^2+X X^2+X  0 X^2+X  X  X X^2+X X^2 X^2+X X^2  X X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  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 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 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 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 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+192x^80+84x^81+386x^82+264x^83+616x^84+440x^85+712x^86+456x^87+756x^88+560x^89+662x^90+552x^91+751x^92+360x^93+492x^94+248x^95+270x^96+92x^97+136x^98+16x^99+62x^100+34x^102+24x^104+8x^106+10x^108+2x^110+5x^112+1x^124

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 56.9 seconds.