The generator matrix

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

generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+22x^135+198x^136+210x^138+282x^139+150x^141+264x^142+48x^144+234x^145+142x^147+240x^148+72x^150+108x^151+6x^153+72x^154+58x^156+36x^157+8x^159+24x^160+2x^162+2x^165+2x^168+2x^171+2x^174+2x^186

The gray image is a linear code over GF(3) with n=216, k=7 and d=135.
This code was found by Heurico 1.16 in 0.134 seconds.