The generator matrix

 1  0  0  1  1 15  9  1  1  1  1  1  1  1  1  1  3  1 21  1 21  1  1 18  1  1  1  1  1  1  6  1 15 24 18  3  1  0  1 15  3  1  9  1
 0  1  0  0  9  1  1 26 22 16  2 16 23  3 14 23  3 13  1  9  1 19  3  1 17 21  4 26 22  2  1 16  1  1  1  1  7  1 25 21  1 22  1  0
 0  0  1  7 17 16 17  0 16 17  2 15  4 11  3 19  1  5  8  3 18 24 14  7 14  4  1  8 17  1  1 12  4 11 24 20 16 10 23  1 15 16  8 19
 0  0  0  9 18  0  0  9  0  0  9 18  0  0 18  9  9 18 18  9  9  0  9 18  0 18  9 18  9 18  0  9  9 18  9  9  9 18 18  0  0 18 18  0

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

Homogenous weight enumerator: w(x)=1x^0+1060x^81+1278x^82+2196x^83+4926x^84+3564x^85+4896x^86+7750x^87+5994x^88+7344x^89+8454x^90+4284x^91+2664x^92+2950x^93+918x^94+396x^95+278x^96+88x^99+8x^102

The gray image is a code over GF(3) with n=396, k=10 and d=243.
This code was found by Heurico 1.16 in 326 seconds.