The generator matrix

 1  0  0  1  1  1  1  1  1 18  1  1 12  9 21  1  1  1  1 15 18  1  1  1  1  1 15  1  1  1  1  1  1  1 15  1  1 24  0  1  6  1  1  1  6  1  1 21  1  1  1  1 21  1 12  6  1  1  9  3 12  1  1  1  1  1  1 24 15  1  1  1
 0  1  0  0  9 16 26 25 26  1  4  2  1  3  1 16 20 13  3  1  1 13 21 18 11  8  1 23 11  6  7 14 15 22  1 12 25  9  1 24  1 12 14  4  1  7  5 24 22 24 18  5  1  9  1  1 14  8  1  1  1  4  6  1 25 14 26  1 12  1 24  0
 0  0  1  7 17 14 26  1 13 16 24 21 23  1 15 17 14  9  2 11  4 25 22  3 19  0 15  4 18 10 13 11  6 23 23 18  6  1 12 17 17 10 23 21  1 12 24  1 14  4  8 16 19 14  0  9  1 15 19  8  5 22  9 17  9  4  4 21  1  1  3 15
 0  0  0  9 18 18 18  9  9  9  0  0 18  9  9  0  9  9  9  0  0 18 18 18  0 18 18 18  9  0  0  0  9 18  9 18 18 18 18  9  0  9  0  9 18 18 18 18  9  0  0  0  0 18  0 18 18  9  9 18  9 18 18  0  0  0 18  0  9  9  0  0

generates a code of length 72 over Z27 who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+244x^135+678x^136+2148x^137+1914x^138+2646x^139+5400x^140+3474x^141+3984x^142+7872x^143+4310x^144+4188x^145+6906x^146+3238x^147+3348x^148+4194x^149+1678x^150+1002x^151+1128x^152+362x^153+168x^154+30x^155+56x^156+18x^157+18x^158+18x^159+12x^162+6x^163+6x^164+2x^168

The gray image is a code over GF(3) with n=648, k=10 and d=405.
This code was found by Heurico 1.16 in 8.27 seconds.