The generator matrix

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

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+750x^138+2502x^141+4544x^144+6342x^147+7678x^150+8684x^153+9060x^156+8162x^159+5848x^162+3532x^165+1454x^168+380x^171+72x^174+16x^177+8x^180+6x^183+6x^186+2x^189+2x^192

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 72.9 seconds.