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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+80x^78+120x^79+228x^80+576x^81+288x^82+534x^83+1618x^84+558x^85+1146x^86+3710x^87+2370x^88+1428x^89+3838x^90+720x^91+786x^92+678x^93+198x^94+126x^95+290x^96+102x^97+108x^98+124x^99+18x^100+12x^101+6x^102+6x^104+6x^105+6x^108+2x^111

The gray image is a code over GF(3) with n=396, k=9 and d=234.
This code was found by Heurico 1.16 in 1.34 seconds.