The generator matrix

 1  0  1  1  1  1  1  3 24  1  1  1  1  3  1  1 21  1  1  1  1  9  1  1 15  1  1  1  1 18  1  1  1  0  1  1  1  0  1  1  1  1  1 18  1  9  1  1 21  1  1  1  0  1  1  3  1  1  3  1 18  1 21  1  1  1  1  3  9  1  1  1  1 24  1 12  1  3
 0  1  1 26 18 25 26  1  1 26 16 21  4  1 18 20  1  5  4  0  7  1 20 24  1 23 10  3  2  1 25 13 14  1  0 26  9  1 19 17 15  6 14  1 14  1  5 18  1 22 21  2  1 25 23  1 23 21  1 13  1  5  1  7 24 12 26  1  1  6  7  0  1  1  5  1  9  3
 0  0 24  0 18  0  0  9  0 18 18  9  9 12 21  6 15 12 15 15 24 12 15 15 21  3 12  3  6 15  3  3 12 21 12 24 24  0 18 21  6  3  9 15  9 18  0  0 12 12 18 12 15 18  6 24  6  6 18 24 15 15 18 21  3 24 12 21  6  9 15 15 18 12  3  9 24  9
 0  0  0  3 21 12  9  3 15  6 24  6 18 15 24 24  9 24 15 12 21  3  3 18  9 12 21  0 18 12  6 18  9  9  3  9 15  3 15  0 21 21 15 18  0  6 21 15  3 18  3  3 21 21 24 15 12 15  6  9  9 24 12 18 18 18  0  0 24 21  9 18 21 12 21 18  9 12

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

Homogenous weight enumerator: w(x)=1x^0+522x^146+510x^147+954x^148+2118x^149+1554x^150+2466x^151+4608x^152+2710x^153+4824x^154+6834x^155+4222x^156+5508x^157+7206x^158+3132x^159+4176x^160+3846x^161+1218x^162+954x^163+630x^164+314x^165+72x^166+234x^167+114x^168+102x^170+40x^171+96x^173+26x^174+36x^176+6x^177+12x^179+4x^183

The gray image is a code over GF(3) with n=702, k=10 and d=438.
This code was found by Heurico 1.16 in 95.3 seconds.