The generator matrix

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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+228x^146+136x^147+288x^149+228x^150+288x^152+66x^153+174x^155+80x^156+156x^158+134x^159+150x^161+4x^162+102x^164+26x^165+60x^167+32x^168+12x^170+6x^171+8x^174+4x^180+2x^183+2x^186

The gray image is a linear code over GF(3) with n=231, k=7 and d=146.
This code was found by Heurico 1.16 in 47.5 seconds.