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

generates a code of length 43 over Z27 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+186x^82+300x^83+102x^84+402x^85+444x^86+120x^87+330x^88+180x^89+2x^90+12x^91+30x^92+16x^93+18x^94+12x^95+18x^97+6x^98+6x^100+2x^111

The gray image is a code over GF(3) with n=387, k=7 and d=246.
This code was found by Heurico 1.16 in 27.2 seconds.