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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+340x^81+546x^84+972x^86+1158x^87+1944x^89+1170x^90+162x^93+156x^96+88x^99+12x^102+10x^108+2x^126

The gray image is a code over GF(3) with n=396, k=8 and d=243.
This code was found by Heurico 1.16 in 27.5 seconds.