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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+54x^78+110x^79+84x^80+96x^81+49x^82+42x^83+12x^84+28x^85+15x^86+8x^87+1x^88+4x^91+5x^92+2x^94+1x^96

The gray image is a linear code over GF(2) with n=324, k=9 and d=156.
This code was found by Heurico 1.16 in 0.19 seconds.