The generator matrix

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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+1272x^88+2292x^89+5610x^90+9090x^91+14700x^92+18098x^93+28062x^94+38232x^95+44708x^96+56172x^97+67950x^98+62966x^99+59628x^100+50238x^101+32470x^102+21438x^103+11106x^104+4498x^105+2046x^106+564x^107+30x^108+132x^109+60x^110+12x^111+36x^112+18x^113+6x^114+6x^116

The gray image is a linear code over GF(3) with n=441, k=12 and d=264.
This code was found by Heurico 1.16 in 390 seconds.