The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 X 1 1 1 0 1 1 1 1 1 1 1 0 1 X 1 2X X 1 1 1 1 1 2X 1 1 1 1 1 0 0 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 X+2 0 1 2X+1 X 2 1 2X+1 2X 2X+1 X+2 2X 0 X 1 X+1 1 2 1 1 2X+1 1 2X+1 2 1 1 2X+2 1 1 X+2 X 1 X X
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X X X X X 2X 0 X X 0 X X 0 2X 2X 2X X 2X 0 2X 0 X 0 2X X X 2X X 0 X 0 X X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X X X 2X X X 0 0 2X X 2X 2X X 0 X X 2X 2X 0 X 2X 0 X X 2X X 0 0 2X 2X 2X 0 X 0 2X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X X 2X 2X 2X 2X X X 0 2X 2X 2X 0 0 0 0 0 2X 2X 0 X 2X X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 0 2X 2X 0 X X 2X X X 0 2X 0 0 X X X 0 0 0 X X X 2X X 2X 0 0 X 2X X X 0 0 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 2X 2X X 0 2X 0 2X 2X 2X X 0 2X X 0 2X X 0 2X 2X 0 2X 2X 0 2X 0 X 2X 0 0 2X 0 X X 0 0
generates a code of length 50 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+108x^84+12x^85+42x^86+166x^87+204x^88+330x^89+246x^90+564x^91+552x^92+188x^93+1026x^94+1236x^95+234x^96+1266x^97+1680x^98+238x^99+2148x^100+2028x^101+222x^102+1872x^103+1704x^104+216x^105+1068x^106+852x^107+168x^108+474x^109+282x^110+122x^111+114x^112+42x^113+122x^114+70x^117+60x^120+18x^123+6x^126+2x^129
The gray image is a linear code over GF(3) with n=150, k=9 and d=84.
This code was found by Heurico 1.16 in 4.96 seconds.