The generator matrix

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

generates a code of length 50 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+38x^78+6x^79+186x^81+48x^82+18x^83+348x^84+198x^85+222x^86+422x^87+546x^88+750x^89+542x^90+1494x^91+1794x^92+528x^93+2850x^94+3360x^95+632x^96+4620x^97+5574x^98+608x^99+5850x^100+6186x^101+686x^102+5334x^103+4710x^104+678x^105+3372x^106+2586x^107+672x^108+1518x^109+912x^110+484x^111+366x^112+132x^113+344x^114+42x^115+218x^117+106x^120+44x^123+14x^126+8x^129+2x^132

The gray image is a linear code over GF(3) with n=150, k=10 and d=78.
This code was found by Heurico 1.16 in 37.7 seconds.