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

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+136x^78+170x^80+80x^82+64x^84+40x^86+20x^88+1x^128

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 5.21 seconds.