The generator matrix

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

generates a code of length 75 over Z27 who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+588x^138+1230x^139+4266x^140+6594x^141+8880x^142+13368x^143+19144x^144+21276x^145+31008x^146+36440x^147+37446x^148+49110x^149+53924x^150+46884x^151+51252x^152+45920x^153+33024x^154+28302x^155+19408x^156+10098x^157+7110x^158+3472x^159+1386x^160+708x^161+306x^162+90x^163+18x^164+66x^165+42x^166+12x^167+18x^168+18x^169+12x^170+14x^171+6x^172

The gray image is a code over GF(3) with n=675, k=12 and d=414.
This code was found by Heurico 1.16 in 640 seconds.