The generator matrix

 1  0  0  1  1  1  1  1  1  1 21 15  1  1  1  1  0  1  1  1  1 21  3  1 15  1  1  1  1  1  1  1  9  1  1 12  3  1 18  1  1 18  9  1  1  3  1  9  1 21  1  1  1
 0  1  0  0  9 16 16  1  2 23  1  1 23 18 10  8  1 21  5  8  1  1  1  1  3  8 15 14 20  9 16 10  1 21 22  1 12 16  1  3  8  0  1 22  6  1 20  1  9  1 23 17  3
 0  0  1  1 17 17 15  1 23  3 17 19  4 15 16  2 19 26  4  0 24 14 18 20  1  9  4 23  7 16  8 10 22  6  6 15  1 21  6 15 25  1 23 12 10  2 21 16 13 14  4  2  7
 0  0  0 24 18  9  0  6  3 12  9  9  0 15 21 18 12 21  6 24 12  6 21 15 21  9 21 24 12 24  3 18  6  3  9 15  9  6 15 18 15  3 21 24  0  0 15 24 12  0 18 24 24

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

Homogenous weight enumerator: w(x)=1x^0+380x^96+738x^97+1518x^98+4356x^99+4842x^100+6210x^101+11434x^102+11466x^103+12936x^104+21588x^105+19932x^106+17946x^107+23326x^108+14988x^109+9846x^110+8848x^111+3582x^112+1464x^113+1090x^114+210x^115+102x^116+124x^117+78x^118+36x^119+46x^120+54x^121+6x^123

The gray image is a code over GF(3) with n=477, k=11 and d=288.
This code was found by Heurico 1.16 in 50.8 seconds.