The generator matrix

 1  0  1  1  1  1  1 21  1  1 24  1  1  1  1  1  0  1  1  1 21  1  1 24  1  1  1 24  1  1  1  0  1  1 21  1  1  1  0  1  1  1 24  1  1  1  1 21  1  1  1  1  1  1  1  1  1  6 12  1  1  3  1  9  9  1  1  1  0
 0  1  7 26 21  4 20  1 19 24  1 23 26 16  0  4  1 19 21 20  1 23 24  1 16 26 19  1 23 21  0  1  4 20  1 24 12 13  1 16 26 21  1 20 16 23  0  1  8  9 12 11 26  8  3 18  4  1  1  7  0  1 22  1  1  5  7  4  1
 0  0  9  0  0  0 18  9 18  9  9  9  9  0 18  0  0  9  9 18  0 18  9  0 18 18 18  9  9  0  0 18  0  9  9  0  9  0  0  0 18  9  9 18 18  0 18  9  0  0 18  0 18 18 18  0 18 18 18  0 18  9 18  9 18  0 18 18 18
 0  0  0  9  0  9  9  9 18 18  0 18  0  9  9  0  9  9  0  9 18  9  0 18  9  0  0 18  0  9 18  9 18  9  0 18  9 18  9  0 18  9 18 18 18  0 18  9 18  0  0 18  0  9 18  9  9  0 18  0 18  0 18 18 18  9  9  9 18
 0  0  0  0 18 18  0 18 18  9 18 18  9  9  9  9  0  0  0 18  9  9 18  0  0 18  0  9 18  0  0  9 18  9  9  9  9  9 18 18  9 18  0 18  9 18 18  9  0  9 18 18  0  9  9  9  0  9  0  0  0  0 18  9  9 18 18  9 18

generates a code of length 69 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+80x^129+324x^130+468x^131+390x^132+1620x^133+1056x^134+1132x^135+1620x^136+1740x^137+1830x^138+2592x^139+1596x^140+1400x^141+2268x^142+708x^143+152x^144+324x^145+150x^146+58x^147+96x^149+20x^150+18x^152+20x^153+8x^156+8x^159+4x^165

The gray image is a code over GF(3) with n=621, k=9 and d=387.
This code was found by Heurico 1.16 in 1.32 seconds.