The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  1  1  1  0  1  1  1  0  1  3  0  6  1  1  1
 0  1  1  8  0  1  8  1  0  7  8  1  7  0  8  1  3  7  8  1  7  1  1  1  0  0  0
 0  0  6  0  0  0  0  0  0  0  0  0  0  3  3  6  3  3  3  3  6  6  6  6  3  0  0
 0  0  0  3  0  0  0  0  3  6  3  6  3  6  6  0  0  3  6  0  3  6  0  0  3  0  0
 0  0  0  0  3  0  0  3  6  6  3  3  0  6  6  6  6  6  6  3  0  0  0  0  3  3  0
 0  0  0  0  0  6  0  6  3  0  3  3  6  6  3  6  0  0  0  3  6  0  0  6  0  6  0
 0  0  0  0  0  0  3  6  0  6  6  3  3  6  6  3  6  3  3  3  6  6  6  0  6  6  0

generates a code of length 27 over Z9 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+54x^39+24x^41+144x^42+270x^44+296x^45+774x^47+616x^48+2256x^50+1238x^51+3564x^53+1706x^54+3816x^56+1426x^57+1986x^59+686x^60+432x^62+222x^63+118x^66+38x^69+16x^72

The gray image is a code over GF(3) with n=81, k=9 and d=39.
This code was found by Heurico 1.16 in 1.84 seconds.