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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+296x^132+18x^134+602x^135+180x^137+840x^138+1692x^140+1058x^141+5328x^143+1136x^144+5328x^146+984x^147+576x^149+832x^150+468x^153+174x^156+106x^159+28x^162+22x^168+4x^171+8x^177+2x^189

The gray image is a code over GF(3) with n=648, k=9 and d=396.
This code was found by Heurico 1.16 in 31.8 seconds.