The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  0  1  1  1  1 21  1  1 24  1  1  1  9  1  1  1 12  1  1  1 24  1  1  1  6  1  1  1  1 24  1  1  6  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  7 26 21  4 20  1 24 19 23  1 16  0 26  1 21 20 24  4  1 19 23  1  9 16  8  1 12 13  5  1 24 19 20  1 10 11  6  1 11 24 19 10  1  6 20  1  0 21  6  0  9 21  9 12 18 16  7  4 10  3  4 10 16 13  7  7 26  8 23 11
 0  0  9  0 18  9 18  0  9 18  0  9  0 18  9 18  9 18  0  0  9 18  9 18  9 18 18  9  0 18 18 18 18  9  9  0  0  9 18  0  0  0  9  0 18  9  0  9  0 18 18  9  9  0 18  9  0 18  0  0 18 18  9  9  0 18  9 18  0  9  9  0
 0  0  0  9  0  9  9  9 18 18  0 18  9  9  0  9  9 18 18 18  0  0 18 18 18 18 18 18 18  0  9 18  0  9 18  9  9  0  9  0  0  0  0 18  9  9  9  0 18  9 18  9  0  0  0 18  9  0  0  9  9 18  0 18 18 18  9  9 18 18  0 18

generates a code of length 72 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+152x^138+348x^139+684x^140+560x^141+930x^142+540x^143+762x^144+450x^145+162x^146+580x^147+588x^148+504x^149+120x^150+114x^151+54x^152+6x^156+2x^168+2x^180+2x^186

The gray image is a code over GF(3) with n=648, k=8 and d=414.
This code was found by Heurico 1.16 in 0.277 seconds.