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

generates a code of length 75 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+844x^144+4860x^150+576x^153+278x^162+2x^225

The gray image is a code over GF(3) with n=675, k=8 and d=432.
This code was found by Heurico 1.16 in 5.49 seconds.