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

generates a code of length 71 over Z3[X]/(X^2) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+54x^129+100x^132+36x^133+120x^135+90x^136+86x^138+360x^139+98x^141+450x^142+60x^144+396x^145+32x^147+126x^148+34x^150+36x^153+30x^156+26x^159+20x^162+10x^165+8x^168+6x^171+4x^174+2x^177+2x^195

The gray image is a linear code over GF(3) with n=213, k=7 and d=129.
This code was found by Heurico 1.16 in 0.195 seconds.