The generator matrix

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

generates a code of length 44 over Z27 who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+376x^87+162x^88+186x^90+2x^108+2x^114

The gray image is a code over GF(3) with n=396, k=6 and d=261.
This code was found by Heurico 1.16 in 0.387 seconds.