The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  X  1  1  1  1  1  1  1  X  1  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0 2X  X 2X  X 2X  X 2X  X  0 2X  0 2X  X  0  X  X 2X  X  X 2X  X  0  X  0  X  0 2X 2X  0  0  X 2X  X  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X 2X 2X  0  X  0 2X  X  X  0  X 2X  0  X 2X  X  0  X 2X 2X 2X  0 2X  X  0  0  0 2X  0 2X 2X 2X  X 2X  0  X  0
 0  0  0  X  0  0  0  0  0  X  X 2X 2X 2X  0 2X  0  X  X  0  X 2X  0  0  0  0 2X 2X  X  X  0  X  0  0  0 2X  0  X  X 2X 2X 2X 2X 2X  0  0 2X  X  0  0
 0  0  0  0  X  0  0  0  X 2X 2X 2X  X  X 2X 2X  X 2X  0  0  0 2X  0  0  X 2X  0  0  X 2X 2X 2X 2X  0  0 2X 2X  0  X  0 2X 2X  X 2X  X 2X  X 2X  0  0
 0  0  0  0  0  X  0  0 2X 2X  X  X  0 2X  0  X  X  0  X  X  0  0  X  0  0  X 2X 2X  X  X 2X 2X  X  X 2X  0 2X  0  X  X  X 2X  0 2X  X  0  X  0  X  0
 0  0  0  0  0  0  X  0 2X  X 2X  X 2X  0  0  0  0  X 2X 2X 2X  0  X  X 2X  X  X  0  X 2X  X 2X  X  0  X  0 2X 2X 2X  X 2X  0  X  X  X  X  X  0 2X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  0 2X 2X 2X 2X 2X  0  0  X  X 2X 2X  0  0 2X  0 2X 2X  0  X  0 2X  0  X 2X  X  X  0  0 2X  0 2X 2X  0 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+54x^78+168x^81+334x^84+428x^87+18x^88+490x^90+216x^91+610x^93+1080x^94+640x^96+2880x^97+618x^99+4320x^100+654x^102+3456x^103+720x^105+1152x^106+596x^108+496x^111+330x^114+244x^117+118x^120+40x^123+14x^126+2x^129+2x^132+2x^135

The gray image is a linear code over GF(3) with n=150, k=9 and d=78.
This code was found by Heurico 1.16 in 7.85 seconds.