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  0  1  1  3  1  1  1  1 15  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 24 10 18  1 10  7  1 19  1 22
 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  1 19 11  7 13 26  0  5  8 18
 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  0 18 18 18 18 18  0 18 18

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

Homogenous weight enumerator: w(x)=1x^0+920x^81+1728x^82+2142x^83+3786x^84+5112x^85+4428x^86+6678x^87+7776x^88+6426x^89+7272x^90+5940x^91+2718x^92+2124x^93+1314x^94+324x^95+270x^96+78x^99+12x^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 97.6 seconds.