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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+294x^137+334x^138+564x^140+478x^141+162x^142+1128x^143+1132x^144+324x^145+930x^146+544x^147+276x^149+38x^150+90x^152+56x^153+90x^155+74x^156+18x^158+6x^159+6x^161+8x^162+6x^167+2x^192

The gray image is a code over GF(3) with n=648, k=8 and d=411.
This code was found by Heurico 1.16 in 0.452 seconds.