The generator matrix

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

generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+66x^154+108x^155+34x^156+150x^157+162x^158+34x^159+54x^160+8x^162+42x^163+54x^164+12x^166+2x^186+2x^210

The gray image is a linear code over GF(3) with n=237, k=6 and d=154.
This code was found by Heurico 1.16 in 0.12 seconds.