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

generates a code of length 42 over Z27 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+62x^81+234x^82+126x^84+180x^85+30x^87+72x^88+18x^90+6x^96

The gray image is a code over GF(3) with n=378, k=6 and d=243.
This code was found by Heurico 1.16 in 0.0245 seconds.