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  3  1  3  1  3  1  1  3  3  1
 0  9  0  0  0  0  0  0  0  0  9 18 18  9  9  9  0 18  9 18  9  0 18  0  9  9  0 18  9 18 18 18  9  9  0 18  9  9  9  9  0  0  0  9 18  0 18  9 18 18  0  0  9
 0  0  9  0  0  0  0  9 18 18 18  0  0 18  9 18  9  0  9  9  0 18  9  0 18  9 18  0  9  0 18 18 18  9  0 18  9 18 18  9  9 18 18  9  0  9  9  0  9 18  0  0 18
 0  0  0  9  0  0  9 18  0 18  0  0 18  9  9 18  0  9  0 18  0 18 18  0 18  0  9 18 18  9  9  9 18  0 18 18  0  0 18  9  0  9  0  9 18 18  0 18 18  0  9  9 18
 0  0  0  0  9  0 18 18  9  0 18 18 18  0 18 18  0 18  9  0 18 18 18  9  0  0 18  9  0  9  0  9  0 18 18  0  9  9  9  9 18  0 18 18  0 18  0  0 18 18  0  0  9
 0  0  0  0  0  9 18 18 18 18 18 18  9 18  9  9 18  9 18 18 18 18  0 18  0  9  0  0 18  9 18  0 18  9  9  9  9  9  9  0  0  0 18  9  9  9  0  0 18  9  0 18  0

generates a code of length 53 over Z27 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+172x^96+178x^99+270x^102+648x^105+4374x^106+494x^108+216x^111+84x^114+34x^117+62x^123+20x^126+6x^132+2x^144

The gray image is a code over GF(3) with n=477, k=8 and d=288.
This code was found by Heurico 1.16 in 84.3 seconds.