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

generates a code of length 74 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+62x^144+24x^145+72x^146+186x^147+1584x^148+72x^149+118x^150+18x^152+30x^153+12x^154+6x^156+2x^222

The gray image is a code over GF(3) with n=666, k=7 and d=432.
This code was found by Heurico 1.16 in 0.174 seconds.