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  3  1  1  1  1  1  1  1  1  1  3  1  1  1  0  1  1  3  1  1  3  0  1  1  3  1  3  1  1  1  1  0  1  1
 0  3 24  0 21 24  0 21 24  9 21 24  6  0 21 12  6  9 24  0 21 12  0 24  9  3  6 15  9 24  0 21 18 12 24  9  6 21  3  3  0  6 15  0 21 18  3 24  6 18 21  3 21 24 21 18  0 24  3  6  6 21  0 21 18 12  3 18  3 18 21
 0  0  9  0  0  0  0 18  9  0  9 18 18  0  0  9  0  0  9 18 18  9  9 18 18  9  0 18 18  9 18 18 18 18 18  9 18 18 18  0 18 18  9  0  0 18  0 18  0  0  0 18 18 18 18  9 18  9 18  0 18  9  0  0 18 18  9  9  9  9 18
 0  0  0  9  0  0  0  0  0 18  0  9 18  9  9  9  9 18  9 18  9  9  0 18  9  0  9  9 18 18  9 18  0 18  0  9  9  9  9  9  0  9  9  0 18 18 18 18 18  0 18  0 18  9  0  0  0 18  0  0 18  0  0  0  9  9  0  0  9 18  0
 0  0  0  0 18  0  9 18  9  9  0  9 18  0 18  0 18  0 18 18  0  0 18  9  9  0  0 18 18 18  0 18 18  9  0 18  9  0  0  9 18  9 18 18  9  9  0 18 18  9  9 18  9  0  9  0  0 18 18  0  0  9 18  0 18 18  9  0  9 18  9
 0  0  0  0  0  9  9  0 18  9  0  0  9  9 18 18  9  9  0 18  0  0 18  9  9  9  9  0  9  0  9 18  0  9  9  0  9 18  9  0 18 18  9  9  0 18  0  0  9  0 18 18 18  0 18 18  9  9  0  0  0 18  0  9 18  9  0  9 18 18 18

generates a code of length 71 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+136x^129+78x^131+336x^132+66x^133+222x^134+456x^135+324x^136+660x^137+1026x^138+1260x^139+1524x^140+2468x^141+2334x^142+1950x^143+2420x^144+1620x^145+1092x^146+504x^147+198x^148+174x^149+320x^150+30x^151+96x^152+188x^153+30x^155+78x^156+6x^158+32x^159+10x^162+16x^165+8x^168+12x^171+4x^174+2x^177+2x^186

The gray image is a code over GF(3) with n=639, k=9 and d=387.
This code was found by Heurico 1.16 in 2.69 seconds.