The generator matrix

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

generates a code of length 82 over Z27 who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+658x^153+996x^154+2316x^155+3880x^156+4998x^157+6102x^158+8950x^159+9150x^160+11844x^161+14460x^162+14394x^163+16344x^164+17490x^165+14550x^166+14064x^167+12180x^168+8412x^169+6276x^170+4548x^171+2574x^172+1182x^173+962x^174+252x^175+138x^176+164x^177+18x^178+42x^179+64x^180+18x^181+12x^182+60x^183+36x^184+6x^187+6x^189

The gray image is a code over GF(3) with n=738, k=11 and d=459.
This code was found by Heurico 1.16 in 83.4 seconds.