The generator matrix

 1  0  0  1  1  1  1  1  1  1 24  1 21  1 21  0  1  1  1 15  1  1 18  1  1  1  1 24  1 18  1  1  6 24  1  1  6  1  1  1 12  1  1  9  1  1  1  1  1  0  1 15  1  1  6  6  1  1  1  1 18  1 15  0  1  1  1
 0  1  0  0  9 16 16 14  1 14  1 17  1 18  9  1 13 17 25  1 26  6  1 23 10 24 20 12 25  1 21 22  1  1 24 21  1 17 11 10 24  5  1  1 24  2 19  1 23  1  1  1 14 17  1  1  6  4 13 20  1  2 24  1  2  9  0
 0  0  1  1 17 17 15 16  7 21 13 20 17  0  1 13  4 26  5 23 25 22 12 18 21 17  4  1  5  5 21  7 24 10  5 10 22 26  3 25  1  3 13  9 21 24 20  2 22 26  1 25  7  6 24 12  5  2 11 11 26 11  1 13 13  5  9
 0  0  0 24 18  9  0  9  0 18  0 18  9 15  6  6  3 21 21 21  3  0 12 12  3 12 15 21 24 24 21 15  6  3  3  3  3 24 24 15  3 21 18  3  0  9  9 21  9  3 18  0 24 12  9 24 15 18 24 21  6 15 24 12 12 21 18

generates a code of length 67 over Z27 who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+272x^123+618x^124+1938x^125+2294x^126+4488x^127+6882x^128+6098x^129+9564x^130+13860x^131+12962x^132+16518x^133+21042x^134+14798x^135+17280x^136+18282x^137+9810x^138+8646x^139+6066x^140+2606x^141+1446x^142+792x^143+304x^144+168x^145+108x^146+134x^147+60x^148+36x^149+42x^150+12x^151+6x^152+6x^153+6x^154+2x^156

The gray image is a code over GF(3) with n=603, k=11 and d=369.
This code was found by Heurico 1.16 in 66.1 seconds.