The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+18x^77+46x^78+62x^79+88x^80+96x^81+81x^82+64x^83+22x^84+14x^85+16x^86+2x^87+1x^88+1x^154

The gray image is a linear code over GF(2) with n=324, k=9 and d=154.
This code was found by Heurico 1.16 in 0.291 seconds.