The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^123+168x^124+474x^125+798x^126+1470x^127+1830x^128+2712x^129+3120x^130+4446x^131+4298x^132+5598x^133+7098x^134+6210x^135+5880x^136+5154x^137+3754x^138+2700x^139+1536x^140+568x^141+336x^142+216x^143+154x^144+102x^145+72x^146+110x^147+48x^148+66x^149+44x^150+18x^151+6x^152+16x^153

The gray image is a code over GF(3) with n=603, k=10 and d=369.
This code was found by Heurico 1.16 in 9.76 seconds.