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

generates a code of length 67 over Z27 who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+34x^120+54x^121+78x^122+142x^123+108x^124+162x^125+308x^126+174x^127+198x^128+442x^129+708x^130+210x^131+3646x^132+2160x^133+180x^134+6742x^135+2172x^136+222x^137+616x^138+186x^139+174x^140+242x^141+144x^142+144x^143+102x^144+84x^145+60x^146+44x^147+24x^148+24x^149+22x^150+18x^151+10x^153+6x^155+14x^156+16x^159+8x^162+2x^165+2x^189

The gray image is a code over GF(3) with n=603, k=9 and d=360.
This code was found by Heurico 1.16 in 2.47 seconds.