The generator matrix

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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+666x^138+2508x^141+4818x^144+6132x^147+7824x^150+8694x^153+8898x^156+7812x^159+6254x^162+3456x^165+1500x^168+396x^171+72x^174+12x^177+6x^180

The gray image is a linear code over GF(3) with n=231, k=10 and d=138.
This code was found by Heurico 1.16 in 115 seconds.