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

generates a code of length 69 over Z27 who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+312x^127+426x^128+1976x^129+2820x^130+4080x^131+6404x^132+8496x^133+8916x^134+13706x^135+13986x^136+14538x^137+18838x^138+17964x^139+15072x^140+16618x^141+12414x^142+7806x^143+6446x^144+3240x^145+1506x^146+702x^147+366x^148+90x^149+108x^150+132x^151+36x^152+52x^153+48x^154+18x^155+30x^156

The gray image is a code over GF(3) with n=621, k=11 and d=381.
This code was found by Heurico 1.16 in 68.5 seconds.