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

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

Homogenous weight enumerator: w(x)=1x^0+502x^144+18x^145+108x^146+1230x^147+126x^148+540x^149+1782x^150+630x^151+1602x^152+2634x^153+1224x^154+2538x^155+2670x^156+900x^157+1026x^158+846x^159+18x^160+18x^161+526x^162+390x^165+234x^168+86x^171+30x^174+2x^180+2x^198

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 2.69 seconds.