The generator matrix

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

generates a code of length 47 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+132x^78+60x^79+366x^80+512x^81+306x^82+888x^83+878x^84+732x^85+2034x^86+1842x^87+1518x^88+3372x^89+2972x^90+2352x^91+5136x^92+3828x^93+2820x^94+5616x^95+4174x^96+2724x^97+4686x^98+3002x^99+1650x^100+2814x^101+1484x^102+768x^103+1044x^104+560x^105+180x^106+270x^107+164x^108+12x^109+18x^110+72x^111+38x^114+18x^117+2x^120+4x^123

The gray image is a linear code over GF(3) with n=141, k=10 and d=78.
This code was found by Heurico 1.16 in 32.4 seconds.