The generator matrix

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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+430x^78+2446x^81+5094x^84+7620x^87+10842x^90+12266x^93+10780x^96+6636x^99+2288x^102+552x^105+70x^108+8x^111+4x^114+12x^117

The gray image is a linear code over GF(3) with n=138, k=10 and d=78.
This code was found by Heurico 1.16 in 32.6 seconds.