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

generates a code of length 76 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+166x^144+528x^147+2148x^150+3120x^153+240x^156+78x^159+32x^162+204x^165+42x^168+2x^225

The gray image is a code over GF(3) with n=684, k=8 and d=432.
This code was found by Heurico 1.16 in 0.524 seconds.