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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+88x^123+48x^124+96x^125+240x^126+144x^127+222x^128+434x^129+312x^130+642x^131+584x^132+1212x^133+2946x^134+666x^135+2226x^136+4890x^137+688x^138+1566x^139+1080x^140+414x^141+144x^142+198x^143+198x^144+114x^145+126x^146+188x^147+66x^148+6x^149+68x^150+24x^153+18x^156+16x^159+10x^162+4x^165+2x^171+2x^180

The gray image is a code over GF(3) with n=612, k=9 and d=369.
This code was found by Heurico 1.16 in 2.55 seconds.