The generator matrix

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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+210x^84+66x^85+540x^86+1296x^87+984x^88+3072x^89+2838x^90+2772x^91+7218x^92+6358x^93+5208x^94+9774x^95+6046x^96+3450x^97+5124x^98+2398x^99+492x^100+450x^101+408x^102+108x^103+54x^104+86x^105+30x^106+12x^107+26x^108+12x^109+8x^111+4x^114+2x^117+2x^123

The gray image is a linear code over GF(3) with n=423, k=10 and d=252.
This code was found by Heurico 1.16 in 6.81 seconds.