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

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+252x^137+192x^138+420x^140+162x^141+246x^143+150x^144+120x^146+84x^147+180x^149+42x^150+108x^152+40x^153+72x^155+28x^156+48x^158+12x^159+6x^161+14x^162+6x^164+2x^180+2x^183

The gray image is a linear code over GF(3) with n=216, k=7 and d=137.
This code was found by Heurico 1.16 in 1.05 seconds.