The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  3  1
 0  3  0  0  0  0  0  0  0  0  0  0  0  0  6  3  6  3  3  3  6  6  3  0  3  3  3  0
 0  0  3  0  0  0  0  0  0  0  0  3  3  3  6  6  0  6  3  0  3  6  6  6  0  3  3  0
 0  0  0  3  0  0  0  0  0  3  3  6  6  6  0  6  0  0  3  6  3  3  6  0  0  0  6  6
 0  0  0  0  3  0  0  0  3  6  6  6  6  0  6  6  3  6  3  6  3  3  3  3  3  0  0  6
 0  0  0  0  0  3  0  0  6  6  3  6  0  3  0  6  3  0  3  3  0  6  0  3  3  0  6  3
 0  0  0  0  0  0  3  0  6  3  6  0  6  3  0  3  0  3  3  3  3  3  3  6  3  3  0  6
 0  0  0  0  0  0  0  3  3  0  3  3  6  3  6  0  6  0  0  6  6  0  6  6  0  3  3  3

generates a code of length 28 over Z9 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+112x^39+240x^42+396x^45+622x^48+486x^50+694x^51+2916x^53+920x^54+5832x^56+1032x^57+3888x^59+960x^60+780x^63+464x^66+204x^69+90x^72+38x^75+8x^78

The gray image is a code over GF(3) with n=84, k=9 and d=39.
This code was found by Heurico 1.16 in 3.07 seconds.