The generator matrix

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

generates a code of length 45 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+72x^78+54x^79+72x^80+256x^81+126x^82+114x^83+468x^84+168x^85+252x^86+618x^87+294x^88+306x^89+830x^90+348x^91+366x^92+670x^93+264x^94+234x^95+466x^96+138x^97+108x^98+162x^99+66x^100+6x^101+36x^102+28x^105+18x^108+12x^111+4x^114+2x^120+2x^126

The gray image is a linear code over GF(3) with n=135, k=8 and d=78.
This code was found by Heurico 1.16 in 0.467 seconds.