The generator matrix

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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+336x^147+642x^150+430x^153+246x^156+192x^159+160x^162+50x^165+48x^168+44x^171+32x^174+4x^180+2x^183

The gray image is a linear code over GF(3) with n=231, k=7 and d=147.
This code was found by Heurico 1.16 in 0.755 seconds.