The generator matrix

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

generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+264x^137+156x^138+396x^140+166x^141+282x^143+166x^144+180x^146+108x^147+78x^149+70x^150+90x^152+20x^153+84x^155+24x^156+48x^158+14x^159+24x^161+12x^164+2x^180+2x^186

The gray image is a linear code over GF(3) with n=216, k=7 and d=137.
This code was found by Heurico 1.13 in 0.0987 seconds.