The generator matrix

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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+74x^81+76x^82+84x^83+76x^84+82x^85+48x^86+36x^87+6x^88+8x^89+9x^90+5x^92+4x^95+1x^98+1x^102+1x^106

The gray image is a linear code over GF(2) with n=336, k=9 and d=162.
This code was found by Heurico 1.11 in 0.172 seconds.