The generator matrix

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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+274x^84+642x^85+1866x^86+2176x^87+4098x^88+5148x^89+4532x^90+5928x^91+7416x^92+6260x^93+7572x^94+6048x^95+3010x^96+1938x^97+1350x^98+432x^99+210x^100+36x^101+58x^102+12x^103+6x^104+22x^105+12x^106+2x^111

The gray image is a linear code over GF(3) with n=414, k=10 and d=252.
This code was found by Heurico 1.16 in 5.18 seconds.