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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+162x^151+42x^153+378x^154+18x^156+54x^157+12x^159+54x^160+2x^162+6x^168

The gray image is a linear code over GF(3) with n=693, k=6 and d=453.
This code was found by Heurico 1.16 in 0.235 seconds.