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^2  1  1 X^2  1  1  X  X  1  1  1  1  0 X^2+X  1  1 X^2+X  1  0  X  1  1  1  1 X^2+X  1 X^2  1  1  1  1 X^2  1  1  X X^2  1  X  1  X  1  1 X^2+X  1  1  1  1  1  1  0 X^2+X  1  1  1  1  0  0 X^2  1  1  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 X^2+X X^2+X+1  1  X X+1  1  1  X  1 X+1  0  1  1 X^2+X X^2+X+1  1  0  1  1 X^2+1 X+1 X^2  1  1  X  1 X^2+X X^2+X+1  0 X^2+X  1  1 X+1  1  X  X X^2 X^2+X+1 X^2+X X^2+X X^2+X+1  1  X X^2 X^2 X^2+X X+1 X^2+1  1  1  X X^2+1 X^2+X+1 X+1  1  X  1 X^2+X X^2+X+1  1  1  0
 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+X X+1  X X^2  1  1 X+1  0  X X+1 X^2+1  1 X^2+X+1 X^2+X X^2 X+1  1 X^2+X X^2 X^2  1 X^2+X+1  X X^2+1  X X^2+X+1 X^2 X^2+1 X^2+X  0 X^2+X X^2+1 X^2+X+1  0 X^2+X+1 X^2+X X^2 X^2+1  X X+1 X^2+X  1 X^2+X+1  X  X  0  X  0  0  X X+1 X^2+1 X^2+X+1  0  X X^2+1 X^2+1 X^2+X X^2+X X+1  1 X+1  X X+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+32x^78+116x^79+162x^80+68x^81+34x^82+28x^83+4x^84+12x^86+32x^87+8x^88+8x^89+4x^93+1x^96+2x^98

The gray image is a linear code over GF(2) with n=324, k=9 and d=156.
This code was found by Heurico 1.11 in 0.157 seconds.