The generator matrix

 1  0  0  0  1  1  1 18  1  1  1  1  1 15 12  1  1  3  1  1  1  1  1  9  1  1  1  1  1 12  1  1  1  1  1  3 12  1 21  1 24  1  1  1  1  1  1  1 15  1 15  3  1  1  1 15  1  1  1  1  1  1  1  6  1  1  1
 0  1  0  0 18  1 19  1 18  0 26 23 22 24  1 12  2  1 12 10  7  8 14  1  2  6 13 23 23  1 13 15 26 21 10  1 18  7  1 24  1 14 16  5 11 18 15  9  1 11 15  6  7 11 19 12 12 18  3 19 11  2 17  1 21 25  3
 0  0  1  0 16 25 14  7  4 23 12 13 11  1  5 20  8 18  0 22  6 10  6 13 24 12 15 11  8 26 18 13  7 26  2  0  1 22  2 21  7 14 16  7 19 12 23 22 24  9  1  1 21  2 20 21  7 11 22 16 15 18  0 20  7  3 15
 0  0  0  1 14  9  5  5 22 24  1  6 16 23  2  5 13  4 20  7 17  2  2  1  0  7 12  3 26  6  4 18  7 25 15  5 13 23  7 22 21 18 12 17  4 20 16  8  6 12 24  5 14  2 26  1 10 21 24 12 24 20 10 25  2  0 24

generates a code of length 67 over Z27 who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+450x^122+906x^123+2994x^124+5238x^125+9170x^126+11694x^127+15576x^128+22818x^129+29046x^130+36270x^131+43042x^132+49458x^133+54594x^134+56260x^135+50184x^136+46608x^137+37102x^138+25770x^139+15120x^140+9602x^141+5388x^142+2292x^143+1122x^144+336x^145+168x^146+38x^147+48x^148+72x^149+30x^151+30x^152+2x^153+12x^154

The gray image is a code over GF(3) with n=603, k=12 and d=366.
This code was found by Heurico 1.16 in 533 seconds.