The generator matrix

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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+36x^142+78x^143+96x^144+276x^145+528x^146+274x^147+1344x^148+1512x^149+784x^150+3420x^151+3288x^152+2116x^153+7278x^154+5340x^155+2814x^156+9294x^157+5604x^158+2468x^159+5682x^160+3060x^161+772x^162+1548x^163+810x^164+32x^165+216x^166+120x^167+26x^168+42x^169+54x^170+18x^171+24x^172+18x^173+14x^174+16x^177+8x^180+12x^183+18x^186+4x^189+4x^192

The gray image is a code over GF(3) with n=702, k=10 and d=426.
This code was found by Heurico 1.16 in 13.9 seconds.