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

generates a code of length 61 over Z27 who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+152x^114+102x^115+72x^116+288x^117+114x^118+432x^119+228x^120+90x^121+3780x^122+174x^123+48x^124+576x^125+134x^126+42x^127+84x^129+18x^130+68x^132+66x^133+72x^135+6x^136+8x^138+2x^141+2x^147+2x^174

The gray image is a code over GF(3) with n=549, k=8 and d=342.
This code was found by Heurico 1.16 in 0.335 seconds.