The generator matrix

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

generates a code of length 49 over Z3[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+414x^89+530x^90+720x^91+2106x^92+2644x^93+2754x^94+3894x^95+5496x^96+6696x^97+5754x^98+7994x^99+7056x^100+5010x^101+3748x^102+1728x^103+1230x^104+588x^105+366x^107+124x^108+138x^110+16x^111+24x^113+18x^116

The gray image is a linear code over GF(3) with n=441, k=10 and d=267.
This code was found by Heurico 1.16 in 6.84 seconds.