The generator matrix

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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+64x^81+30x^82+18x^83+288x^84+228x^85+426x^86+542x^87+1308x^88+2826x^89+1300x^90+5028x^91+8028x^92+2058x^93+9258x^94+10776x^95+2160x^96+6576x^97+5490x^98+1156x^99+828x^100+108x^101+268x^102+72x^103+30x^104+92x^105+34x^108+28x^111+12x^114+8x^117+4x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=423, k=10 and d=243.
This code was found by Heurico 1.16 in 6.81 seconds.