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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+62x^78+24x^79+90x^80+268x^81+444x^82+504x^83+1286x^84+2364x^85+1674x^86+5464x^87+6726x^88+3222x^89+10564x^90+8910x^91+3204x^92+7146x^93+4656x^94+1404x^95+446x^96+162x^97+90x^98+180x^99+42x^100+18x^101+34x^102+18x^105+28x^108+8x^111+4x^114+2x^117+4x^120

The gray image is a linear code over GF(3) with n=405, k=10 and d=234.
This code was found by Heurico 1.16 in 6.43 seconds.