The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  0 2X  1  0  1  1  X 2X  1  1  X  1  1  1  0  1  1  1  1  1 2X 2X 2X  1  1 2X  1  1 2X  0  1  X 2X 2X
 0  1  0  0  0  1  2  1 2X+1  2 2X+2  1  1  0  1  0  1  1  X 2X 2X+2  1 2X+1 X+2 2X+1  1  2  X  0 2X X+2  1  1  1 X+1 2X  0 X+2  X  1  1  1  1 2X  1
 0  0  1  1  2  2  2  1 2X  0 2X+1  2 2X+1  0 2X 2X+1  1 X+2  1 2X+2  1  1  2  2  0 X+2  0 2X  X 2X+2 2X  0  X X+1 2X+2 X+2  1  0 X+1  X  2 2X+2 X+2  1  2
 0  0  0 2X  0  0  0  0  0 2X 2X  X 2X 2X 2X  0 2X 2X  X  X 2X  0  X  0  0 2X  0 2X 2X  0  X 2X 2X  0 2X  0  0 2X 2X  X 2X 2X  0 2X  0
 0  0  0  0  X  0  X 2X 2X 2X 2X  0  X  X 2X  X  X  X  X 2X 2X  0 2X  0  X 2X  X  X 2X 2X 2X  X 2X 2X 2X  0 2X 2X  0  X  0  X  X  0  0
 0  0  0  0  0 2X  X  X  0  X  0  X  X  X  X 2X 2X  0 2X 2X 2X 2X  0  0  X 2X 2X 2X  0 2X  0 2X 2X  X  0 2X 2X 2X 2X  X 2X  0 2X  X  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+318x^78+222x^79+186x^80+764x^81+360x^82+480x^83+1386x^84+540x^85+672x^86+1802x^87+852x^88+978x^89+2202x^90+948x^91+912x^92+2006x^93+786x^94+780x^95+1562x^96+432x^97+294x^98+656x^99+150x^100+66x^101+164x^102+78x^103+6x^104+44x^105+6x^106+20x^108+8x^111+2x^117

The gray image is a linear code over GF(3) with n=135, k=9 and d=78.
This code was found by Heurico 1.16 in 53 seconds.