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

generates a code of length 96 over Z27 who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+90x^190+378x^191+10x^192+198x^194+6x^195+18x^197+2x^198+18x^199+2x^201+4x^204+2x^213

The gray image is a code over GF(3) with n=864, k=6 and d=570.
This code was found by Heurico 1.16 in 3.88 seconds.