The generator matrix

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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+108x^79+114x^80+280x^81+474x^82+294x^83+614x^84+930x^85+504x^86+956x^87+1362x^88+690x^89+1078x^90+1734x^91+1026x^92+1454x^93+1686x^94+804x^95+1138x^96+1308x^97+648x^98+696x^99+924x^100+246x^101+236x^102+192x^103+42x^104+52x^105+30x^106+6x^107+22x^108+12x^111+14x^114+2x^117+6x^120

The gray image is a linear code over GF(3) with n=138, k=9 and d=79.
This code was found by Heurico 1.16 in 6.82 seconds.