The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+144x^80+108x^81+211x^82+56x^83+204x^84+20x^85+74x^86+28x^87+51x^88+16x^89+31x^90+28x^91+22x^92+16x^94+5x^96+4x^98+3x^100+1x^104+1x^108

The gray image is a linear code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.11 in 0.266 seconds.