The generator matrix

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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+22x^78+18x^79+48x^80+98x^81+96x^82+462x^83+460x^84+282x^85+1764x^86+1368x^87+2442x^88+6042x^89+3272x^90+7560x^91+10002x^92+4294x^93+7584x^94+7758x^95+2396x^96+834x^97+1524x^98+292x^99+120x^100+66x^101+84x^102+18x^103+36x^104+40x^105+28x^108+20x^111+8x^114+8x^117+2x^120

The gray image is a linear code over GF(3) with n=414, k=10 and d=234.
This code was found by Heurico 1.16 in 6.56 seconds.