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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+252x^149+174x^150+438x^152+206x^153+234x^155+120x^156+186x^158+82x^159+114x^161+48x^162+84x^164+30x^165+48x^167+30x^168+60x^170+24x^171+24x^173+8x^174+18x^176+2x^177+4x^183

The gray image is a linear code over GF(3) with n=234, k=7 and d=149.
This code was found by Heurico 1.16 in 3.44 seconds.