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

generates a code of length 42 over Z27 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+72x^84+6x^93+2x^99

The gray image is a code over GF(3) with n=378, k=4 and d=252.
This code was found by Heurico 1.16 in 0.0167 seconds.