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

generates a code of length 70 over Z27 who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+224x^129+564x^130+1686x^131+3306x^132+4146x^133+6876x^134+7782x^135+9198x^136+12684x^137+14116x^138+15702x^139+18516x^140+17792x^141+16026x^142+15420x^143+11850x^144+7980x^145+6666x^146+3288x^147+1596x^148+732x^149+472x^150+126x^151+42x^152+104x^153+30x^154+54x^155+84x^156+30x^157+18x^158+30x^159+6x^160

The gray image is a code over GF(3) with n=630, k=11 and d=387.
This code was found by Heurico 1.16 in 69.6 seconds.