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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+342x^134+256x^135+18x^136+786x^137+568x^138+234x^139+1170x^140+1590x^141+1296x^142+1788x^143+3182x^144+2466x^145+1734x^146+1896x^147+360x^148+654x^149+210x^150+378x^152+152x^153+258x^155+90x^156+102x^158+54x^159+66x^161+18x^162+12x^164+2x^192

The gray image is a code over GF(3) with n=648, k=9 and d=402.
This code was found by Heurico 1.16 in 10.8 seconds.