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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+204x^79+330x^80+122x^81+600x^82+798x^83+668x^84+1320x^85+1932x^86+1996x^87+3018x^88+2928x^89+2104x^90+1524x^91+780x^92+134x^93+348x^94+300x^95+56x^96+198x^97+180x^98+14x^99+72x^100+42x^101+6x^102+6x^103+2x^111

The gray image is a code over GF(3) with n=396, k=9 and d=237.
This code was found by Heurico 1.16 in 1.25 seconds.