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

generates a code of length 54 over Z27 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+56x^96+18x^98+120x^99+72x^101+122x^102+180x^104+96x^105+468x^107+4442x^108+576x^110+62x^111+144x^113+44x^114+38x^117+32x^120+30x^123+32x^126+14x^129+8x^132+2x^135+2x^138+2x^147

The gray image is a code over GF(3) with n=486, k=8 and d=288.
This code was found by Heurico 1.16 in 0.342 seconds.