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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+126x^83+40x^84+480x^86+104x^87+486x^88+708x^89+78x^90+54x^92+12x^93+78x^95+4x^96+12x^98+2x^102+2x^126

The gray image is a code over GF(3) with n=396, k=7 and d=249.
This code was found by Heurico 1.16 in 0.0503 seconds.