The generator matrix

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

generates a code of length 19 over Z27 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+162x^36+324x^38+216x^39+18x^42+6x^45+2x^54

The gray image is a code over GF(3) with n=171, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0168 seconds.