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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 142.

Homogenous weight enumerator: w(x)=1x^0+30x^142+96x^143+80x^144+162x^145+258x^146+122x^147+276x^148+348x^149+434x^150+378x^151+894x^152+2040x^153+468x^154+2358x^155+3972x^156+588x^157+2394x^158+2636x^159+534x^160+366x^161+34x^162+258x^163+336x^164+32x^165+108x^166+174x^167+30x^168+78x^169+48x^170+26x^171+30x^172+18x^173+12x^174+20x^177+6x^178+4x^180+14x^183+10x^186+2x^189+6x^192+2x^204

The gray image is a code over GF(3) with n=702, k=9 and d=426.
This code was found by Heurico 1.16 in 97 seconds.