The generator matrix

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

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+51x^80+92x^81+138x^82+170x^83+83x^84+84x^85+88x^86+62x^87+84x^88+62x^89+41x^90+16x^91+11x^92+16x^93+7x^94+6x^95+2x^96+2x^97+4x^98+2x^99+1x^122+1x^126

The gray image is a linear code over GF(2) with n=340, k=10 and d=160.
This code was found by Heurico 1.16 in 0.391 seconds.