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  1  1  1  1  1  1  1  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  1  3  1  0  1  1  1  1  3  3  1  1  1  1  1  3  1  0  1  3  1  3
 0  3  0  0  0 24 21 15  3  6 24 21 21  9 15  3 12 18 15  0 24  3 21 24 18 24  0 24  9  3  3  9  9 15 12 18 12  3  6 24 18 21 15  9  0  6 24 21 24 21  6 24  9 12  3  3 15 24  3  3 21 21 15 21 24  9  3  9  9 18  3  6 24  3  0 24  0  3
 0  0  3  0  9 18  9 18  0  0 24 12  6  6 12  6 15  3  3  3 15  3 12 24 24 12 24  9  3  9  6 21  6  6 12  6  3 15 12  0  6  0  6  9 21  9  9 12  3  9 12 15  0  9  0 15 15 15 12 18  3 24  0 21 12  6 18  6 21  3 15 18 21 24 18  6 18 21
 0  0  0  3 15  0  6  3 12 15  9  9 18  0 18  3  6  6 12 21 21 12 24 24 24  6 21 21 24 24  0  9  6  3 21  0 24 24 18  9 12  3 18 21 21 21  6  0  3 18 15 24  6  6  6 12 18  0 24  0  9  6  9 21 21 24 24  9 12  9 12 12  0  9 18  6 15  6

generates a code of length 78 over Z27 who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+336x^146+232x^147+18x^148+912x^149+612x^150+360x^151+1362x^152+1192x^153+1242x^154+2274x^155+2572x^156+2196x^157+2376x^158+1350x^159+558x^160+636x^161+290x^162+360x^164+142x^165+246x^167+108x^168+108x^170+36x^171+108x^173+6x^174+30x^176+18x^177+2x^207

The gray image is a code over GF(3) with n=702, k=9 and d=438.
This code was found by Heurico 1.16 in 9.41 seconds.