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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+138x^145+324x^146+18x^147+414x^148+468x^149+54x^150+558x^151+852x^152+164x^153+2850x^154+1674x^155+3188x^156+5268x^157+1590x^158+166x^159+306x^160+276x^161+20x^162+234x^163+306x^164+12x^165+216x^166+174x^167+14x^168+180x^169+90x^170+2x^171+36x^172+54x^173+4x^174+6x^175+18x^176+6x^179+2x^225

The gray image is a code over GF(3) with n=702, k=9 and d=435.
This code was found by Heurico 1.16 in 2.82 seconds.