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

generates a code of length 75 over Z27 who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+66x^137+166x^138+276x^140+328x^141+594x^143+780x^144+1092x^146+2326x^147+2688x^149+3662x^150+2694x^152+2640x^153+726x^155+680x^156+378x^158+148x^159+168x^161+88x^162+60x^164+52x^165+6x^167+18x^168+14x^171+12x^174+2x^177+10x^180+2x^183+2x^189+2x^192+2x^198

The gray image is a code over GF(3) with n=675, k=9 and d=411.
This code was found by Heurico 1.16 in 23.1 seconds.