The generator matrix

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

generates a code of length 74 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+204x^138+750x^139+936x^140+1518x^141+2754x^142+2340x^143+3070x^144+4920x^145+4770x^146+4098x^147+6402x^148+5940x^149+4610x^150+5724x^151+4086x^152+2484x^153+2028x^154+792x^155+522x^156+396x^157+90x^158+152x^159+150x^160+50x^162+126x^163+54x^165+66x^166+2x^168+12x^169+2x^171

The gray image is a code over GF(3) with n=666, k=10 and d=414.
This code was found by Heurico 1.16 in 18.4 seconds.