The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+750x^76+1578x^77+4326x^78+7092x^79+12222x^80+19202x^81+27126x^82+36390x^83+47688x^84+61242x^85+67680x^86+69660x^87+64338x^88+48768x^89+32658x^90+17478x^91+8208x^92+3486x^93+1206x^94+78x^95+84x^96+84x^97+30x^98+42x^99+18x^100+6x^101

The gray image is a linear code over GF(3) with n=387, k=12 and d=228.
This code was found by Heurico 1.16 in 322 seconds.