The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  3  1  0  1  1  1  3  1  3  1  0  0  1  1  1  1
 0  3  0  0 24 21 15  3 24 21 18  0 21 15  9 24 15 21  3  3 12 18 18  6  9 12 24 24 21 21 15 18 15  0  6 12 18 12 15  6 21 15 18  3 18  6 12  6  0 21  9 18 21  9 21 15  3 15  6  0 24 18 24 12  3  0 21 18 12  9
 0  0  3 24  0 15 21  3  6  6 21  0  3 21 15 18  6  9  3 18  6 24  0  3 21 12  9 24 15  0 18 15  3  9 15 12 21  9 24  0 15 12 12 21  6  9  6 21 15  9  0 18  0  6 15 24 15 15  9 21 15 24  0 21  9  3  6 15 15 18
 0  0  0  9  0  0 18  0  0  9 18  9 18  9 18  9  9  9 18  0  0  0 18  0  9 18  0 18 18 18 18 18 18  9  0  0 18  0  9  0 18  9  9  9  0  9  9  0  0 18 18  0  0 18 18  9 18  0 18  9  9 18  9  0  9  9  9  9  9 18
 0  0  0  0  9 18  0  9 18  0 18  9  0  0  0  9 18 18 18  9  9  0  9  0  9  9  0 18  0 18 18  9  9 18  0 18  0 18  0 18 18  9  0  0  9 18  9 18 18  0 18  9 18 18  9  9  0  9  0 18 18  0  0 18  0  0  9  0  0  9

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

Homogenous weight enumerator: w(x)=1x^0+144x^129+162x^130+144x^131+476x^132+168x^133+594x^134+568x^135+540x^136+1884x^137+1626x^138+1590x^139+3450x^140+2578x^141+1488x^142+2310x^143+490x^144+144x^145+108x^146+230x^147+144x^148+126x^149+240x^150+90x^151+66x^152+132x^153+36x^154+60x^155+52x^156+12x^157+6x^158+18x^159+4x^162+2x^189

The gray image is a code over GF(3) with n=630, k=9 and d=387.
This code was found by Heurico 1.16 in 2.41 seconds.