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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+52x^96+158x^99+208x^102+18x^104+204x^105+180x^107+240x^108+720x^110+192x^111+1440x^113+13322x^114+1440x^116+164x^117+576x^119+182x^120+160x^123+168x^126+104x^129+74x^132+52x^135+14x^138+12x^141+2x^156

The gray image is a code over GF(3) with n=513, k=9 and d=288.
This code was found by Heurico 1.16 in 2.81 seconds.