The generator matrix

 1  0  1  1  1  1  1  3  1  1 24  1  1  1  3  1  1  1  1  1  3  1 15  1  1  1 12 21 12  1  1 24  1  1  6  1  1  1  1  1  1  3  1  1
 0  1  1 26 18 25 26  1  4 26  1  0  4  0  1 23 25  2 24  1  1 12  1 17 10 26  1  1  1 14 15  1 21  6  1  4 24 10 19 21 11  1  6 14
 0  0 24  0 18  0  0  9 18 18  0 21  6  6  3 24 12 12  6 24 24 21 21 21 12  6 15 15  3 21  3  9 18  9 12 15  6 18  9  3 24 12 15  6
 0  0  0  3 21 12  9  3 24  6 15 21 15 18  6 24  3 12 24  3 12  6  9 15 24  9  6  9 12  0  0 18 18  6  0  9 21  6 12  9 18 12  6  3

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

Homogenous weight enumerator: w(x)=1x^0+258x^79+486x^80+580x^81+1326x^82+2526x^83+2200x^84+4176x^85+6342x^86+6246x^87+6996x^88+9750x^89+6650x^90+5154x^91+3648x^92+982x^93+774x^94+366x^95+72x^96+180x^97+150x^98+32x^99+90x^100+54x^101+4x^102+6x^104

The gray image is a code over GF(3) with n=396, k=10 and d=237.
This code was found by Heurico 1.16 in 7.9 seconds.