The generator matrix

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

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+78x^78+324x^79+62x^81+54x^84+24x^87+162x^88+18x^90+6x^96

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 0.0512 seconds.