The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  0  1  3  1  1  3  0  1  1
 0  3  0  0  0 24 21 15  3  6 24 21 21  9 15  3 12 18 15  0 24  3 21 24 18 24  0 24  9  3  3  9  9 15 12 18 12  3  6 24 18 21 15  9 21  6 24 21 24 15 21 24  6  9  9 15  3  0 21 12  3 15  3 15 18 21  9  6  0 18 15 21  3 24  0 18 24 21  3 12  3
 0  0  3  0  9 18  9 18  0  0 24 12  6  6 12  6 15  3  3  3 15  3 12 24 24 12 24  9  3  9  6 21  6  6 12  6  3 15 12  0  6  0  6  9 15  9  9 12  3 21 24 15 12 21  9 12 24 24  6  9  0 15  6  3  3  0  3 12  3  0 24  9  9  3  0 12  9  6 18 18 15
 0  0  0  3 15  0  6  3 12 15  9  9 18  0 18  3  6  6 12 21 21 12 24 24 24  6 21 21 24 24  0  9  6  3 21  0 24 24 18  9 12  3 18 21  0 21  6  0  3  9 21 24 15  3  9  3 24 18 21  9  6 18  6  9 12  9 24  3 24 18  3  3  9 15 21 15 12 18  0  9  6

generates a code of length 81 over Z27 who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+354x^152+242x^153+744x^155+568x^156+1464x^158+996x^159+972x^160+2364x^161+4568x^162+1944x^163+2532x^164+1114x^165+432x^167+162x^168+336x^170+150x^171+210x^173+128x^174+228x^176+66x^177+42x^179+16x^180+42x^182+6x^183+2x^228

The gray image is a code over GF(3) with n=729, k=9 and d=456.
This code was found by Heurico 1.16 in 3 seconds.