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

generates a code of length 77 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+556x^144+1000x^147+54x^148+2030x^150+324x^151+972x^152+4254x^153+2106x^154+1944x^155+4156x^156+432x^157+628x^159+474x^162+388x^165+274x^168+50x^171+36x^174+2x^177+2x^216

The gray image is a code over GF(3) with n=693, k=9 and d=432.
This code was found by Heurico 1.16 in 3.43 seconds.