The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+236x^80+156x^81+350x^82+92x^83+343x^84+92x^85+188x^86+72x^87+174x^88+36x^89+86x^90+28x^91+71x^92+24x^93+28x^94+26x^96+8x^97+16x^98+10x^100+4x^101+4x^102+3x^104

The gray image is a linear code over GF(2) with n=340, k=11 and d=160.
This code was found by Heurico 1.16 in 1.42 seconds.