The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+102x^80+72x^81+138x^82+188x^83+165x^84+200x^85+112x^86+140x^87+160x^88+184x^89+136x^90+148x^91+101x^92+56x^93+56x^94+36x^95+32x^96+6x^98+5x^100+5x^104+1x^108+3x^112+1x^120

The gray image is a linear code over GF(2) with n=348, k=11 and d=160.
This code was found by Heurico 1.16 in 0.669 seconds.