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

generates a code of length 79 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+40x^144+24x^145+84x^146+230x^147+144x^148+258x^149+456x^150+210x^151+630x^152+972x^153+198x^154+2184x^155+1808x^156+198x^157+3708x^158+2348x^159+192x^160+2508x^161+1512x^162+216x^163+606x^164+314x^165+144x^166+132x^167+158x^168+84x^169+48x^170+86x^171+48x^172+42x^173+30x^174+6x^176+16x^177+20x^180+6x^183+8x^186+4x^189+6x^192+2x^195+2x^198

The gray image is a code over GF(3) with n=711, k=9 and d=432.
This code was found by Heurico 1.16 in 3.1 seconds.