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  3  3  1  3  1  1  1  1  3  1  3  3  1  1  1  1  1
 0  9  0  0  0  0  0  0  0  0  9 18 18  9  9  9  0 18  9 18  9  0  9  0 18  9  0 18  9 18 18 18  9  9  0  9 18 18  0  0  0  9 18  9  9  9 18  9  9  0  9 18 18  9  9  0  9  9 18  9  0  0  9  9  0  0 18  0  0  0  0
 0  0  9  0  0  0  0  9 18 18 18  0  0 18  9 18  9  0  9  9  0 18 18  0  9  9 18  0  9  0 18 18 18  9  0 18 18 18  9  9 18 18 18 18  0 18  0 18  9 18  9 18  9  9 18  9  9 18  9  9  9  9  9  9  9  9  9 18  9  9  0
 0  0  0  9  0  0  9 18  0 18  0  0 18  9  9 18  0  9  0 18  0 18 18  0 18  0  9 18 18  9  9  9 18  0 18  0 18  9  0 18  9 18 18  9  9  0  9  9  0  0  0 18  9 18  0  9  0 18 18  9 18 18 18  9  0  9  9  9  0  0  9
 0  0  0  0  9  0 18 18  9  0 18 18 18  0 18 18  0 18  9  0 18 18  0  9 18  0 18  9  0  9  0  9  0 18 18  0  0 18 18  9  0  9 18  9  0  9  9 18  9  9 18 18 18 18  0  9  0  9  9 18  0  9  9  9  0  0  9 18  9  9  9
 0  0  0  0  0  9 18 18 18 18 18 18  9 18  9  9 18  9 18 18 18 18  0 18  0  9  0  0 18  9 18  0 18  9  9  0  9  0  0  9  0  9 18  9 18  0  0  9  9  0 18  0  0 18  9 18  0  9  0 18  0  0 18  9  9  9  0  9  9  0  9

generates a code of length 71 over Z27 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+4824x^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 code over GF(3) with n=639, k=8 and d=387.
This code was found by Heurico 1.16 in 0.537 seconds.