The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  0  1  1  1  1  1 21  1 24  1  1  1 24  1  1  1  0  1  1 21  1  1  1 24  1  1  1 21  1  1  1  0  1  1 24  1  1  1  1 12  1  1  6  1  0  1  1  1 21  1  1 24  3  1 15  1  1  1  3  1  1  1  1  1  1  1  1
 0  1  7 26 21  4 20  1 24 19 23  1  1  0 16 26 20  4  1 21  1 23 24 19  1  4 26  0  1 16 21  1 20 19 24  1 12 16  4  1 24 20  0  1 21 26  1  6 23 19 24  1 26 16  1 19  1  8 16 23  1 25 10  1  1 21  1  8  6 16  1 10  7 15 23 19  5 20  0
 0  0  9  0  0  0 18 18  9  9  9  0  9  0  9  0  9  9 18 18  9  9  0  9  0 18  0  0  0  0  9 18  0 18  0  0  9 18  0  9 18 18 18 18  9  9 18  0 18 18  0  9 18  9  0  0  0 18 18 18  0  9  0 18  0 18  9 18  9  0  0  9 18 18  9  0 18 18  0
 0  0  0  9  0  0 18 18 18  0  9  9 18  9 18  0 18  9 18  0 18  0 18 18  0  0  0 18 18 18  9 18  9  0 18  9 18 18 18  0  9  0  9  0  9 18  0  0  9  0 18  0  9  9  9 18  0  0 18  9 18 18  9 18  0  0  0  9 18  0  0  9 18  9  0  9 18  9  0
 0  0  0  0 18  0 18  9  9 18 18  9  0  0  0 18  0  0  9  9  9 18 18  9 18  0  9  9  0 18 18 18  0  0 18  0  9 18  0  0  9  9 18  0  9  0  0  9  0 18  9  9  9  9  0  9  9 18  0 18  9  0  9 18  0  0  0 18 18  9  9 18  0  9  9 18  0  0  0
 0  0  0  0  0  9 18  0 18 18 18 18 18 18  9  9 18  0 18  9 18  0  0  0  9  9  9  9  9 18  0 18  9  0  9  9  9  0  9  0  0  0  0  9  0  0 18 18  9  0 18 18  9  0 18  9  9  0  9 18 18  0  9  0 18  0 18  0  9 18  0  9  0  9  0 18  9 18 18

generates a code of length 79 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+42x^144+186x^146+214x^147+342x^148+768x^149+546x^150+1998x^151+1830x^152+1208x^153+5076x^154+3390x^155+2634x^156+8604x^157+4590x^158+3628x^159+9504x^160+4260x^161+1880x^162+4482x^163+1842x^164+492x^165+612x^166+414x^167+162x^168+174x^170+42x^171+36x^173+22x^174+6x^176+12x^177+12x^180+14x^183+8x^186+8x^189+8x^192+2x^198

The gray image is a code over GF(3) with n=711, k=10 and d=432.
This code was found by Heurico 1.16 in 13.2 seconds.