The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+276x^80+236x^82+464x^84+188x^86+406x^88+196x^90+227x^92+20x^94+20x^96+4x^100+4x^104+1x^108+3x^112+2x^120

The gray image is a linear code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 0.654 seconds.