The generator matrix

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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+408x^82+432x^83+2080x^84+2016x^85+1866x^86+2076x^87+2364x^88+2004x^89+1950x^90+1854x^91+768x^92+1214x^93+480x^94+108x^95+18x^96+6x^97+6x^98+26x^99+6x^102

The gray image is a code over GF(3) with n=396, k=9 and d=246.
This code was found by Heurico 1.16 in 0.543 seconds.