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

generates a code of length 68 over Z27 who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+384x^125+522x^126+1890x^127+2838x^128+3996x^129+5772x^130+7872x^131+10014x^132+11940x^133+14136x^134+17092x^135+18714x^136+17412x^137+17668x^138+14952x^139+11724x^140+8026x^141+5520x^142+3348x^143+1482x^144+858x^145+420x^146+146x^147+84x^148+144x^149+68x^150+36x^151+24x^152+28x^153+12x^154+12x^155+6x^156+6x^158

The gray image is a code over GF(3) with n=612, k=11 and d=375.
This code was found by Heurico 1.16 in 67.3 seconds.