The generator matrix

 1  0  0  1  1  1  1  1  9  1  1  1 15  1  1  1  1  3  1 24  1  1  1 12 18  0  1  1  1  1  1 12  1  1 24  1 21  9  1  1  1  1 18  1 12  1  1  1  3  6  1 24  1 15  1  9  1  1  1 21  1  1  1  1 24  1  0  1  1  1 12  1  1 12  1  1  1  1  6  1 15
 0  1  0 18  1 19 23 21  1  4  5 26  1  9 22  7 20  1 16  1 11 24 17  1  1 15 20  3 15  2 10  1 17  3  1  4  1  1  9 23  8  2  1 19 18 16  6 22  3  1 15  1  5  3 18 12 10 12 23  1  9  4 24  5  1 22  1 20 16 19  1 10 22  6  9 12 15 24  1  4  1
 0  0  1 16 25 18 17  8 22  5 22  6 20 21  7  9 23  0 14 13 10 26 11 14 12  1 12 25  0 15 24 17 13  4 12  2 25  2 14 12  7  8 15 19  1 17 25 22  1 19  6 14  2  1 20  1  2  9 15  6 10 19  4 23 18 16  5 16 25  4 20 26 17  1 26 23 20  1 25 15 22

generates a code of length 81 over Z27 who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+1446x^156+918x^157+1734x^158+2994x^159+1374x^160+1152x^161+2240x^162+942x^163+984x^164+2242x^165+672x^166+654x^167+904x^168+330x^169+282x^170+604x^171+132x^172+54x^173+14x^174+6x^175+2x^177+2x^180

The gray image is a code over GF(3) with n=729, k=9 and d=468.
This code was found by Heurico 1.16 in 84.2 seconds.