The generator matrix

 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  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  1  1  1  X  1  X  1  X  1  1  X  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 2X^2  0 2X^2 X^2 2X^2  0 2X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0 X^2 X^2 2X^2 X^2  0 X^2 2X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 2X^2  0 X^2 2X^2  0  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0 X^2 X^2 2X^2 X^2 2X^2  0 X^2 2X^2  0 2X^2  0 X^2 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 X^2 2X^2  0 2X^2  0  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 X^2  0 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 2X^2 2X^2  0 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2  0  0 2X^2 2X^2 2X^2 2X^2 2X^2  0  0  0  0 2X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2  0  0 2X^2 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2  0  0  0 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 2X^2  0 X^2 X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0 2X^2  0 X^2
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2  0  0 2X^2 2X^2  0 2X^2 X^2 2X^2  0  0 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2 2X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 2X^2 2X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 2X^2 X^2 2X^2
 0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2  0 2X^2 2X^2 2X^2  0 X^2 X^2  0 X^2  0  0 2X^2 X^2  0 X^2  0 2X^2  0 2X^2  0  0  0 X^2 X^2 X^2  0 X^2 2X^2  0 2X^2  0 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0  0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+58x^126+174x^129+6x^130+246x^132+12x^133+236x^135+180x^136+210x^138+600x^139+174x^141+1020x^142+13270x^144+1440x^145+176x^147+852x^148+200x^150+264x^151+132x^153+110x^156+100x^159+82x^162+64x^165+32x^168+18x^171+20x^174+2x^177+2x^183+2x^195

The gray image is a linear code over GF(3) with n=648, k=9 and d=378.
This code was found by Heurico 1.16 in 3.86 seconds.