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  9  0  0  0  0  9 18 18  0  0  9  9  9  9  9  9  9  0 18  0 18  0 18  0  9 18  9 18 18  0  0 18  9  0  9 18 18  0 18  9  9  0  0  0  9  9  9  0  9  0  9  0  9  0  0  9  9 18 18 18 18 18 18 18 18  0 18 18 18  9 18  0  0  0
 0  0  9  0  0  9 18  0 18  0  9  9 18 18  0  9  0  9  9  9  9  0  0 18 18  9  9 18  0 18  0  9  9  0 18 18 18  0 18  9  9  0 18 18 18  9 18  0 18  9  0 18  0  9  9  9 18  0  0 18 18  0  9  9  0 18 18  9  0  9  0 18  0  0  0
 0  0  0  9  0 18 18  9  0  9  9  0  0  9 18  9  9 18 18  0  0 18 18 18 18 18  9  9  0  9 18  9 18 18  9 18  9  0  0  0  9  0  0 18  0  0  0  9  9 18 18  0  0  9 18  0 18  9  0 18  9  9  0 18  9  0 18  9 18 18  0 18  9  0  0
 0  0  0  0  9 18 18 18 18 18  0 18  0  0 18 18  0  9  0  0 18 18  9 18  9 18  0 18  0  0 18 18  9  0  0  0 18 18  0  9  9  9  9  0 18  0  9 18 18  0  0 18 18  0  9  9  9  9  9  9  9  9 18 18  0  0 18 18  0  0 18  0  9  9  9

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

Homogenous weight enumerator: w(x)=1x^0+70x^144+24x^147+1986x^150+60x^153+30x^156+12x^159+2x^162+2x^225

The gray image is a code over GF(3) with n=675, k=7 and d=432.
This code was found by Heurico 1.16 in 0.203 seconds.