The generator matrix

 1  0  1  1  1  1  1 21  1 24  1  1  1  1  0  1  1 24  1  1  1  1  1 18  1  1 21  1  1  1  1  0  1  1  3  1  1  1  1  1  1  1 18  1  1  1 24  0  1  1  1  6  1  1  1  1 18 24  1  1  1  1  1  6  1  1  1  1 21 18  1  1  1  3  1  0  1  1
 0  1  1 26 21 24 20  1 23  1 16  4 18 17  1  1  3  1 23 22 26 25  0  1 20 15  1 19 24  4 26  1  0  4  1 18 20 19 12 25 24 17  1 16  2 16  1  1 17 22  7  1  3 23  0 21  1  1 16 17  9 17 11  1 20 22 12 24  1  1  3 17 15  1 12  1  8 20
 0  0 24  0  0  9 18  9  0  9 15 24 21 12 24  3  3  6  6  3  6 12  6 12 15 21 15 24  6 15 18  0  9  9 15  3  6  0  3 12  9 12 12 18 18 15  0  0 18 18 12  6  6 24 24 21 15  3 18 21  0 12  3 21 12 24  3  0 18 18 15  6 24  6  0  3  0 24
 0  0  0  9  0  0  0 18 18  9 18  9 18  9  9  9  0  0 18  0  0 18 18  9  9 18  9  0  0 18  0  0  9 18  9  9  9  9 18 18  9  0  0 18  0  9  0  9 18  9  0 18 18  0 18  9  0  9  9  9  9 18  9  0  0  9  0 18  0 18  0  9  9  9  0  0  0 18
 0  0  0  0 18  9  9  0 18  0 18  9  9  9  9  9  9  9  0  0 18 18 18  9 18  0  0  9  9  9  0  9  0  9 18 18  0  0 18  0  9  0  9  0 18  0 18 18  9  9  9  0  9  0  0  9  0 18 18 18 18  0  0 18  9 18  0  0 18  9 18  9  9  9  0  0 18  0

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

Homogenous weight enumerator: w(x)=1x^0+156x^145+252x^146+406x^147+1116x^148+1578x^149+2286x^150+3264x^151+3006x^152+3826x^153+4818x^154+4380x^155+5866x^156+6714x^157+5124x^158+5314x^159+4368x^160+2328x^161+1734x^162+1002x^163+528x^164+180x^165+222x^166+168x^167+46x^168+114x^169+84x^170+6x^171+54x^172+42x^173+8x^174+30x^175+6x^176+4x^177+12x^178+2x^180+2x^183+2x^189

The gray image is a code over GF(3) with n=702, k=10 and d=435.
This code was found by Heurico 1.16 in 11.9 seconds.