The generator matrix

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

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+210x^78+280x^81+126x^84+36x^87+32x^90+36x^93+6x^96+2x^99

The gray image is a linear code over GF(3) with n=123, k=6 and d=78.
This code was found by Heurico 1.16 in 0.01 seconds.