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

generates a code of length 71 over Z27 who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+174x^134+168x^135+276x^137+288x^138+1284x^140+780x^141+2250x^143+754x^144+156x^146+82x^147+48x^149+42x^150+114x^152+40x^153+54x^155+24x^156+18x^158+6x^159+2x^201

The gray image is a code over GF(3) with n=639, k=8 and d=402.
This code was found by Heurico 1.16 in 18.2 seconds.