The generator matrix

 1  0  1  1  1  1  1  3 24  1  1  1  1  3  1  1  1  1  1  0 21  1  1  1  1  1 18  1  0  1  1  1  1  1  1  1  1  1  1  1  6  1  1  1 24 12  1 12  1 12  1  1  0  1 24  1  1  1  1  1  1  1  1  0  1
 0  1  1 26 18 25 26  1  1 26 16 21  4  1 18 20 12  5 16  1  1 24  7 23 18 23  1  1  1  3  2  9  2 11 16  2 12 10 13  2  1 10 17  8  1  1 16  1  8  1  6  1  1 26  1  3  4 11  1 13  0 17  8  1 15
 0  0 24  0 18  0  0  9  0 18 18  9  9 12 21  6 24 12 24 21 15 15  6  3 12 24 12 21 15  6 18 21 12 18  3  6  6 15 21 12 15 21 12  3 15 15  0 21  6 24 12 21  9 24  9 21  0 21 15  0  6  9 21 24  3
 0  0  0  3 21 12  9  3 15  6 24  6 18 15 24 24  3 24  6  3  9 18  3 12  3  9 18 15 12  6 12  0  0  0  6 12 18  6 21 21  0  9  6  3  6  3 21 21  0  6 18 18  3 15  0  3 18  3  9 15 18 21  9 18  9

generates a code of length 65 over Z27 who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+328x^120+198x^121+534x^122+1988x^123+1800x^124+2298x^125+4020x^126+3024x^127+4632x^128+7248x^129+5154x^130+6024x^131+7806x^132+4860x^133+3246x^134+3236x^135+780x^136+612x^137+532x^138+120x^139+84x^140+220x^141+84x^142+54x^143+58x^144+12x^145+12x^146+64x^147+12x^150+6x^151+2x^153

The gray image is a code over GF(3) with n=585, k=10 and d=360.
This code was found by Heurico 1.16 in 9.53 seconds.