The generator matrix

 1  0  1  1  1  1  1 21  1  1 24  1  1  1  1  1  0  1  1  1 21  1  1 24  1  1  1 24  1  1  1  0  1  1  1  1 21  1  1  1  1 24  0  1  1  9  6  1  1  1  1  1  1 18  1  9  1  6  1  1  6  1  1  1  1  1  1  1  1  1  1  1
 0  1  7 26 21  4 20  1 19 24  1 23 26 16  0  4  1 19 21 20  1 23 24  1 16 26 19  1 23 21  0  1  4 20 24 13  1 19 24  5  8  1  1 21 20  1  1 10 23 26 11  2 12  1  8  1 17  1  6  3  1  0  3 16  1 16  8  4 25  9  6  0
 0  0  9  0  0  0 18  9 18  9  9  9  9  0 18  0  0  9  9 18  0 18  9  0 18 18 18  9  9  0  0 18  0  9  9  0  0 18 18 18  0 18  0 18  9 18  9  9  0  9  0 18  0  9  9  0  9 18 18  9 18  0  9  0  9  0  0 18  0 18  9  9
 0  0  0  9  0  9  9  9 18 18  0 18  0  9  9  0  9  9  0  9 18  9  0 18  9  0  0 18  0  9 18  9 18  9  9 18  9  0  9  0 18  9  9  0 18  0  0 18 18  9  9 18  9  9 18 18  9 18 18  9 18 18  9  0  9  0  0  0  9  0  9 18
 0  0  0  0 18 18  0 18 18  9 18 18  9  9  9  9  0  0  0 18  9  9 18  0  0 18  0  9 18  0  0  9 18  9  9  9 18  9 18  9  0 18  9  0  0 18  0  9  9  0  9 18 18  0 18  0 18  0  9  0 18 18  9 18 18  0  9  0  0  9 18  0

generates a code of length 72 over Z27 who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+48x^135+264x^136+462x^137+1112x^138+1002x^139+1038x^140+1552x^141+1164x^142+1356x^143+3044x^144+1302x^145+1512x^146+2636x^147+1218x^148+792x^149+560x^150+270x^151+102x^152+6x^153+90x^154+78x^155+8x^156+30x^157+6x^158+12x^159+6x^160+2x^162+4x^165+2x^171+2x^174+2x^180

The gray image is a code over GF(3) with n=648, k=9 and d=405.
This code was found by Heurico 1.16 in 1.37 seconds.