The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+270x^77+386x^78+864x^79+1116x^80+1550x^81+1788x^82+2550x^83+2582x^84+2334x^85+2064x^86+1794x^87+1284x^88+630x^89+212x^90+30x^91+96x^92+22x^93+6x^94+78x^95+10x^96+12x^97+2x^99+2x^108

The gray image is a linear code over GF(3) with n=378, k=9 and d=231.
This code was found by Heurico 1.16 in 5.93 seconds.