The generator matrix

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

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+146x^78+294x^79+570x^80+956x^81+1044x^82+1164x^83+2108x^84+1680x^85+2076x^86+3278x^87+2706x^88+3030x^89+4230x^90+3228x^91+3312x^92+4996x^93+3672x^94+3480x^95+4532x^96+2766x^97+2448x^98+2544x^99+1518x^100+1104x^101+1066x^102+498x^103+294x^104+162x^105+84x^106+18x^107+30x^108+6x^109+2x^111+6x^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 37.4 seconds.