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  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  9  0  0  9  0  9  9 18  0  0  9  9  0 18  9 18 18  0  9 18  0  9 18 18 18 18  0  0  0  9  9  0  9  9 18  0  0  9  9  0 18  9 18 18  0  9 18  0  9 18 18 18 18  0  0  9  9  0 18  9  9  9  0  9  9 18  0  0 18  9 18  0 18  9 18  0 18 18 18  0  0  0  9  9  0  9  9 18  0  0  9  9 18 18  0
 0  0  9  0 18  9 18  9 18  0  9  9  0 18  0  0  9  9 18 18 18 18  9  0  0  9 18  0  0  9 18  9  9 18  0 18  0  9  9  0 18  0  0  9  9 18 18 18 18  9  0  0  9 18  0  9 18  9  9  0  9  0 18  9  9  0  9  0 18  0 18 18 18 18  0  9 18  0  9 18  0  0  9 18  9  9 18  0 18  0  9  9  0  0  0 18
 0  0  0  9 18 18  0 18 18 18  9  0 18  0 18  9  9  0  9  9  9 18  9  0  9 18  0  0  9 18 18 18  9  9  9 18 18  0  0  0  9  9 18 18  9  0  0  0 18  9  0 18  0  9  9 18 18 18  9  9  0  0  0  0  9  9 18 18 18  0  9 18  0  9 18  0  9 18  9  0  0  9 18 18 18  9  9  9 18 18  0  0  0  0 18  0

generates a code of length 96 over Z27 who´s minimum homogenous weight is 189.

Homogenous weight enumerator: w(x)=1x^0+14x^189+156x^191+512x^192+18x^195+12x^198+8x^201+2x^210+6x^218

The gray image is a code over GF(3) with n=864, k=6 and d=567.
This code was found by Heurico 1.16 in 0.403 seconds.