The generator matrix

 1  0  1  1  1  1  1  3 24  1  1  1  1  3  1  1 21  1  1  1  1  9  1  1 15  1  1  1  1  3  1  1  6  1  1  1  1 15  1  1  1  1  1  1  1  1  9  1  1  1  1  9  1  1  1  1 21 12 15  1  1  1  1  1  1  1  9  1  1  1  1  3
 0  1  1 26 18 25 26  1  1 26 16 21  4  1 18 20  1  5  4  0  7  1 20 24  1 24 10 12 26  1  9 16  1 20 13  2 14  1  7  1  8 14  9 19 17 24  1 11 18 17 22  1  6  5  2 19  1  1  1  3 12 22 14 26 20 20  1 21 21 22 14 21
 0  0 24  0 18  0  0  9  0 18 18  9  9 12 21  6 15 12 15 15 24 12 15 15 21  3 12  3 24 15 24 12  6 12 18  6 12  3  3  3 21  9  0 18 24  9  0 21  3 21  6 12  3 24  9  3 15 12 24 21  6 24  6  6 12  0 21 12  9 24 15  6
 0  0  0  3 21 12  9  3 15  6 24  6 18 15 24 24  9 24 15 12 21  3  3 18  9 12 21  0  9 12 15 15  6  3  3 18  3  6 15 18  0 21 15  3  6  0  3 18  0 15  0 24 24 21  0  0 24 18 18  9 18 12 24  0  6 21  9  6 24 24  6  0

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

Homogenous weight enumerator: w(x)=1x^0+372x^134+534x^135+648x^136+1842x^137+2028x^138+2934x^139+3216x^140+4116x^141+4446x^142+5352x^143+6000x^144+5886x^145+6228x^146+4930x^147+4140x^148+2388x^149+1656x^150+900x^151+570x^152+228x^153+210x^155+118x^156+156x^158+24x^159+60x^161+32x^162+18x^164+16x^165

The gray image is a code over GF(3) with n=648, k=10 and d=402.
This code was found by Heurico 1.16 in 12.1 seconds.