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

generates a code of length 81 over Z27 who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+150x^154+84x^155+58x^156+168x^157+348x^158+84x^159+1614x^160+324x^161+62x^162+3054x^163+48x^164+30x^165+126x^166+60x^167+6x^168+84x^169+66x^172+30x^173+18x^175+78x^176+30x^178+24x^181+12x^184+2x^237

The gray image is a code over GF(3) with n=729, k=8 and d=462.
This code was found by Heurico 1.16 in 20.3 seconds.