The generator matrix

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

generates a code of length 72 over Z27 who´s minimum homogenous weight is 133.

Homogenous weight enumerator: w(x)=1x^0+396x^133+588x^134+1808x^135+3390x^136+4170x^137+7004x^138+8148x^139+8364x^140+12964x^141+15120x^142+13764x^143+17632x^144+19680x^145+14568x^146+15902x^147+12708x^148+7098x^149+6546x^150+3606x^151+1626x^152+968x^153+504x^154+246x^155+38x^156+72x^157+54x^158+50x^159+30x^160+42x^161+24x^162+6x^163+24x^164+6x^166

The gray image is a code over GF(3) with n=648, k=11 and d=399.
This code was found by Heurico 1.16 in 71.8 seconds.